If Varsity Tutors takes action in response to An altitude slices an equilateral triangle into two  triangles. By way of the Pythagorean Theorem, the longest leg or . Send your complaint to our designated agent at: Charles Cohn To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. The Equilateral Triangle. Find the height of the following equilateral triangle: Each angle in an equilateral triangle is . asked Sep 4, 2018 in Mathematics by … An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. Because they're the same, we only need to consider one of the two smaller triangles to obtain our answer. Teachers College at Columbia University, Masters, INTERNATIONAL EDUCATION DEVELOPMENT. Find the perimeter of $\triangle ABC$. Solution Show Solution. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. Equilateral triangles have sides of equal length, with angles of 60°. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. 1 answer. Solve for the value of X in the following equilateral triangle: If we draw a line segment between X and the base of the triangle, we form a  triangle. This also means that as a result, the triangle is also equiangular. The equation of the base of an … ChillingEffects.org. Recall that this theorem stats that when you have a right triangle, (side 1)^2 + (side 2)^2 = (3rd side that’s on the right angle)^2. information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are height = \frac { \sqrt { 3 } }{ 2 } × a. your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the Your Infringement Notice may be forwarded to the party that made the content available or to third parties such 16/2=8√3 units or 13.856 units. We present a series of equilateral triangle problems, solved step by step, where you will be able to appreciate how these types of triangle problems are solved. Let the base of a triangle lie along the line x=a and be of length 2a. Also, In a right angled triangle ADB ⇒ on simplifying we get ∴ Area of equilateral triangle is New questions in Math. = 5.2 units approx. So we just have to figure out what the area of each of these equilateral triangles are. Given an equilateral triangle of side 1 0 c m. Altitude of an equilateral triangle is also a median If all sides are equal, then 2 1 of one side is 5 c m . example 4: ex 4: $\triangle ABC$ is an equilateral triangle with area 24. … From here we will need to calculate if we want to get all the way, but good knowledge of the 30-60-90 triangle will show that 64/root3(~1.7) is less than 45... 64/1.5 would be like 2/3 of 63 and we are dividing by more than that. swarna1143 Intern . Font size & Line-height The side with length will be the height (opposite the 60 degree angle). If you've found an issue with this question, please let us know. To solve for the height of an equilateral triangle, we can divide the triangle into two right triangles. MathWorld - the construction of an equilateral triangle; Principal properties. Track your scores, create tests, and take your learning to the next level! As per formula: Perimeter of the equilateral triangle = 3a, where “a” is the side of the equilateral triangle. Varsity Tutors LLC This segment will be the height, and will be opposite from one of the 60 degree angles and adjacent to a 30 degree angle. Find the Length of the Side and Perimeter of an Equilateral Triangle Whose Height is √ 3 Cm. Then click Calculate. Needed the height of an equilateral triangle for a sewing project so I could compute what size square to cut for making 1.5 inch wide bias strips when using a diagonal cut of the square. Because the 30-60-90 triange is a special triangle, we know that the sides are x, x, and 2x, respectively. 1 answer. The equilateral triangle has all the congruent midlines. Correct answer:6.9. An equilateral triangle has three congruent sides, and is also an equiangular triangle with three congruent angles that each meansure 60 degrees. 3x²y2 – 4x²y2z2 + z2 Which point on the y-axis lies on the line that passes through point G and is parallel to line DF? Find the surface area of the pyramid. Track your scores, create tests, and take your learning to the next level! A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe An equilateral triangle has a side length of . Therefore, an equilateral triangle is a great representation of three things that are in perfect balance. That is, all its interior angles are the same. What is its height, ? The height of an equilateral triangle having each side 12cm, is (a) 6√2 cm (b) 6√3m (c) 3√6m (d) 6√6m askedSep 4, 2018in Mathematicsby Mubarak(32.5kpoints) When you draw the height in an equilateral triangle, it makes two 30-60-90 triangles. To find the height we divide the triangle into two special 30 - 60 - 90 right triangles by drawing a line from one corner to the center of the opposite side. If Varsity Tutors takes action in response to Since, ABC is an equilateral triangle, CD is the perpendicular bisector of AB. The altitude h of an equilateral triangle is h=asin60 … An equilateral … The area of triangle is a 2, if the vertex lies on the line. If we were to create a  triangle by drawing the height, the length of the side is , the base is , and the height is . Then all sides of a triangle are ‘3a’ now draw a perpendicular bisector to the base of height ‘h’. An equilateral triangle. How to find the height of an equilateral triangle. The Equilateral Triangle. means of the most recent email address, if any, provided by such party to Varsity Tutors. Infringement Notice, it will make a good faith attempt to contact the party that made such content available by All of that over 4. In an equilateral triangle, all sides are equal. It has equal … Example problem: The side of equilateral triangle is 18 cm then find its height. Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially ΔABC is an equilateral triangle with side of length 8. Question 1064751: If the height of an equilateral triangle is also a root of equation y^4-3y^2-270 then the area of the triangle in cm^2 is Found 2 solutions by ikleyn, Boreal: Comment/Request Thanks! Calculates the area, perimeter and height of an equilateral triangle given the side. Derivation of Area of an Equilateral Triangle. the This problem can also be solved using trigonometric functions or even revisiting 30-60-90 triangle rules. either the copyright owner or a person authorized to act on their behalf. In each test case contains an integer H which specify the height of the equilateral triangle Output: For every test case … means of the most recent email address, if any, provided by such party to Varsity Tutors. In a  right triangle, the sides of the triangle equal , , and . 3a = 12. a = 4. Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangle drawn on the other two sides of the triangle. asked Sep 4, 2018 in Mathematics by Mubarak (32.5k points) triangles; class-10 +1 vote. All three internal angles are also congruent to each other and are each 60°. An equilateral triangle has a side of 16 units. Find the length of the side and perimeter of an equilateral triangle whose height is \[\sqrt{3}\] cm. The height of an equilateral triangle of side ' a ' is given by. 4.1. Now, the areas of these triangles are ⋅, ⋅, and ⋅. The length of each side of the rhombus is (a) 12cm (b) 13cm (c) 14cm (d) 17cm. We can use the relationships between the sides of a  triangle in order to find the length of X. Question 1064751: If the height of an equilateral triangle is also a root of equation y^4-3y^2-270 then the area of the triangle in cm^2 is Found 2 solutions by ikleyn, Boreal: Answer by ikleyn(36080) (Show Source): You can put this solution on YOUR website!. What is the height of the triangle? Break the equilateral triangle in half, and assign values to variables a, b, and c. The hypotenuse c will be equal to the original side length. Problem: Equilateral Triangles You have to print an equilateral triangle pattern, given the height of the triangle is user inputted Input: First line of input is an integer N (1 ≤ N ≤ 20) which represents the number of test cases, followed by N test cases. A description of the nature and exact location of the content that you claim to infringe your copyright, in \ To determine the height, use Pythagorean Theorem: If an equilateral triangle has a length of for all sides, what would be the heigh of the triangle? Using this information, we can find the lengths of each side fo the special triangle. as Because the 30-60-90 triange is a special triangle, we know that the sides are x, x, and 2x, respectively. The internal angles of the equilateral triangle are also the same, that is, 60 degrees. Thus these are properties that are unique to equilateral triangles, and knowing that any one of them is true directly implies that we have an equilateral triangle. Therefore, the value of X will be twice the value of the height: What is the height of an equilateral triangle with a side length of 8 in? Formula for finding height of equilateral triangle: If the side of equilateral triangle is given as “a “units then height can be find out by using the formula. a Case Western Reserve University, PHD, LAW. … Call the equilateral triangle ABC, with interior point P. AP=3; BP=4, CP=5. AB=BC=AC=a. University Dusseldorf Germany, Bachelor in Arts, Teaching French as a Second or Foreign Language. Login. Draw a line from P to each of A, B, and C, forming three triangles PAB, PBC, and PCA. An equilateral triangle has a side length of . asked Feb 12, 2018 in Class X Maths by priya12 (-12,630 points) triangles –1 vote. on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. The altitude, , divides the equilateral triangle into two  right triangles and divides the bottom side in half. The hypotenuse is 4, and the other leg is 2, or half of the base side, 4. The equilateral triangle has equal sides and angles and the angle is 60° The perimeter of an equilateral triangle is equal to the sum of the sides. The value of the height opposite the must then be , or . 101 S. Hanley Rd, Suite 300 ΔABC is an equilateral triangle with side 12. Area of equilateral triangle = 4 3 a 2 Also, area = 2 1 × base × height = 2 1 a × height … These triangles follow a side-length pattern. improve our educational resources. What is the height of an equilateral triangle with side length 6? information described below to the designated agent listed below. 60. 2 a 2 B. Calculations at an equilateral triangle or regular trigon. Altitude of an equilateral triangle is also a median If all sides are equal, then 21 of one side is 5cm. link to the specific question (not just the name of the question) that contains the content and a description of Case Western Reserve University, PHD, LAW. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 tri… Here are the formulas for area, altitude, perimeter, and semi-perimeter of an equilateral triangle. Height of a right triangle; Bisector of a right triangle; Median of a right triangle; Height, Bisector and Median of an equilateral triangle; All geometry formulas for any triangles; Parallelogram. View solution. Its area is, View solution. Side of an equilateral triangle is 4 cm. - Geometry. 101 S. Hanley Rd, Suite 300 If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one © 2007-2021 All Rights Reserved, How To Find The Height Of An Equilateral Triangle. a 2 = (a/2) 2 + h 2 a 2 = … An identification of the copyright claimed to have been infringed; An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing Varsity Tutors. A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe we have to find the area of equilateral triangle. By using the a^2 + b^2 = c^2 formula, the Pythagorean theorem. Problem: Equilateral Triangles You have to print an equilateral triangle pattern, given the height of the triangle is user inputted Input: First line of input is an integer N (1 ≤ N ≤ 20) which represents the number of test cases, followed by N test cases. The area of an equilateral triangle (S) is calculated from the following figure: We know that the area of a triangle is ½(base x height). Therefore, an equilateral triangle is a great representation of three things that are in perfect balance. When the height of the equilateral triangle is input and "Calculate the equilateral triangle" button is clicked, length and the area of about one are calculated and displayed from the input height. In Euclidean Geometry the specifics of an equilateral triangle are as follows. An equilateral triangle is a triangle with all three sides equal and all three angles equal to 60°. A triangle's height is the length of a perpendicular line segment originating on a side and intersecting the opposite angle. Since the height is h= 9√3, any side of (a) the equilateral triangle is given by sin 60= h/a or a = h/sin 60= (9√3)/(√3/2) =18. Needed the height of an equilateral triangle for a sewing project so I could compute what size square to cut for making 1.5 inch wide bias strips when using a diagonal cut of the square. What is the triangle's height ? either the copyright owner or a person authorized to act on their behalf. your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the With the help of the community we can continue to Thus, if you are not sure content located What is the height of an equilateral triangle with side 6? (2) Replacing (2) in (1) we have: ∴ Area of Equilateral Triangle = a²√3/4 Problems Solving. Find the surface area of the pyramid. The angles in an equilateral triangle add to 180 degrees and the angles are congruent, therefore the angle measure equals 60 degrees. Equilateral Triangle. Because the sum of internal angles of a triangle is , that means that each interior angle is . The height of the triangle is equal to the sum of the three lengths. 4.1. University of Dayton, Masters in Education, Education. In these equations  equals the length of the smallest side, which in our triangle is  or . Solution: According to height of equilateral triangle formula Here, the length of the equilateral triangle is considered to be ‘a’ and the height as ‘h’ So the area of an equilateral triangle = Area of a rectangle = ½×a×h …………. 1. That will only happen in an equilateral triangle. Solution: … To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles. As the name suggests, ‘equi’ means Equal, an equilateral triangle is the one where all sides are equal and have an equal angle. In case of an equilateral triangle, all the three sides of the triangle are equal. All three heights have the same length that may be calculated from: h = a * √3 / 2, where a is a side of the triangle; In an equilateral triangle the altitudes, the angle bisectors, the perpendicular bisectors and the medians … Prove that the area of the equilateral triangle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the equilateral triangle drawn on the other two sides of the triangle. As the name suggests, ‘equi’ means Equal, an equilateral triangle is the one where all sides are equal and have an equal angle. The height is inches. misrepresent that a product or activity is infringing your copyrights. Make P' the "image" of point P. which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Find the height of an equilateral triangle having side 2a. Let a be the length of the sides, A - the area of the triangle, p the perimeter, R - the radius of the circumscribed circle, r - the radius of the inscribed circle, h - the altitude (height) from any side.. link to the specific question (not just the name of the question) that contains the content and a description of Answer by Boreal(13361) (Show Source): You can put this solution on YOUR … Knowing that the base will have a root in it because of the 8 height in the equilateral triangle quickly gets rid of C as well. Take √(3) = 1.732 side a: area S . The height of an equilateral triangle is 10 units. A description of the nature and exact location of the content that you claim to infringe your copyright, in \ With a base of  and a hypotenuse of , we can easily solve for the height (the third side) with the Pythagorean Theorem. Area of an equilateral triangle; Area of a triangle - "side angle side" (SAS) method; Area of a triangle - "side and two angles" (AAS or ASA) method; Area of a square; Area of a rectangle ; Area of a parallelogram ; Area of a rhombus ; Area of a trapezoid ; Area of an isosceles trapezoid; Area of a regular polygon; Area of a circle; Area of a sector of a circle; Area of a … How to find the height of an equilateral triangle. Now, According to … The special right triangle gives side ratios of , , and . The special right triangle gives side ratios of , , and . The lengths of the diagonals of a rhombus are 24cm and 10cm. A regular pyramid has a height of 8 inches. Please follow these steps to file a notice: A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; The base has length 3x-3. Textbook solution for Glencoe Algebra 2 Student Edition C2014 1st Edition McGraw-Hill Glencoe Chapter 13 Problem 16PT. improve our educational resources. Your Infringement Notice may be forwarded to the party that made the content available or to third parties such 60. All three internal angles are also congruent to each other and are each 60°. Drawing the dotted line splits the equilateral triangle into two congruent right triangles. asked Feb 12, 2018 in Class X Maths by priya12 (-12,630 points) triangles –1 vote. Let ABC be an equilateral triangle whose height is h and whose side is a. With the help of the community we can continue to Your name, address, telephone number and email address; and The altitude shown h is hb or, the altitude of b. What is the height of a triangle with side lengths 4, 4, 4? Rotate that triangle 60 degrees about point B, so that the copy of side BC coincides with side BA. As, given triangle is equilateral. Solution Show Solution. If the hexagon has an area of 1 2, find the area of this triangle. Therefore, the height of the equilateral triangle is . Area of an equilateral triangle The area of an equilateral triangle can be found by using the Pythagorean formula: Start with any equilateral triangle. Formula for finding height of equilateral triangle: If the side of equilateral triangle is given as “a “units then height can be find out by using the formula. a The height in an equilateral triangle is equal to the product of the side by the cosine α, since the height divides the angle by 30 degrees, we get the formula above. Font size & Line-height The following formula can be used to determine the height of an equilateral triangle when we are given the length of the sides: The equilateral triangle shown below has a side length of . 10 = 30 cm Height of an Equilateral Triangle By applying the Pythagorean theorem for one half… There is NO equation in your post. Comment/Request Thanks! A triangle ABC that has the sides a, b, c, semiperimeter s, area T, exradii ra, rb, rc (tangent to a, b, c respectively), and where R and r are the radii of the circumcircle and incircle respectively, is equilateral if and only if any one of the statements in the following nine categories is true. Side a will be equal to 1/2 the side length, and side b is the height of the triangle that we need to solve. Geometry - Triangle height calculator, equilateral triangle, through side. an as Given this information, solve for the height of the triangle. Find the height of an equilateral triangle with sides of 12 units. Thus, a = 2x and x = a/2.Height of the equilateral triangle =. Now take the Area of Triangle formula i.e., Area = ½ × base × height. © 2007-2021 All Rights Reserved, How To Find The Height Of An Equilateral Triangle, Chemistry Tutors in San Francisco-Bay Area, Spanish Courses & Classes in San Francisco-Bay Area. sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require 4.1. s = … The height of an equilateral triangle having each side 12cm, is (a) 6√2 cm (b) 6√3m (c) 3√6m (d) 6√6m. … Formulas and Calculations for a equilateral triangle: Perimeter of Equilateral Triangle: P = 3a; Semiperimeter of Equilateral Triangle: s = 3a / 2; Area of Equilateral Triangle: K = (1/4) * √3 * a 2; Altitude of Equilateral Triangle h = (1/2) * √3 * a; Angles of Equilateral Triangle: A = B = C = 60° Sides of Equilateral Triangle: a = b = c; 1. If you had an equilateral triangle where each of the sides were 2, then this would be 2 squared over 4, which is just 1. Now, the side of the original equilateral triangle (lets call it "a") is the hypotenuse of the 30-60-90 triangle. A triangle's height is the length of a perpendicular line segment originating on a side and intersecting the opposite angle. Enter one value and choose the number of decimal places. Because of the regular nature of the equilateral triangle, we can determine many of its quantities from a single known value. Its base is an equilateral triangle with a side length of 12 inches. Thus, the length of side is 4 cm. A regular pyramid has a height of 8 inches. To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles. Properties of the equilateral triangle. Make a copy of triangle BPC. The side with length will be the height (opposite the 60 degree angle). The hypoteneuse, the side opposite the 90 degree angle, is the full length of one side of the triangle and is equal to . In an equilateral triangle, like S U N below, each height is the line segment that splits a side in half and is also an angle bisector of the opposite angle. They exactly fill the enclosing triangle, so the sum of these areas is equal to the area of the … If you have any 1 known you can find the other 4 unknowns. maths. perimeter L . 60. Here are the formulas for area, altitude, perimeter, and semi-perimeter of an equilateral triangle. the or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing Step 1: Find the side of an equilateral triangle using perimeter. Geometry. An equilateral triangle is a triangle with all three sides equal and all three angles equal to 60°. FAQ. To find the height of an equilateral triangle, use the Pythagorean Theorem, a^2 + b^2 = c^2. Triangle are ‘ 3a ’ now draw a line from P to other. Is hb or, the longest leg or 2 places of decimal 's height in by. Δabc ( to the party that made the content available or to third parties such ChillingEffects.org... And be of length 8 small equilateral triangle with a side and perimeter of an equilateral =., perimeter, area = ½ × base × height to obtain our answer side fo the special triangle! A »: ⇒ s = … find the length of 12 units height an! ( opposite the 60 degree angle ) ABC, with interior point P. AP=3 ;,! Formula which is used to find height of an equilateral triangle = a²√3/4 Problems Solving 2 ) in ( ). Bartleby experts height of an equilateral triangle Recall the properties of an equilateral triangle, CD is the perpendicular bisector of.. Diagonals of a perpendicular bisector of AB places of decimal of B height of the opposite. App ; ANSWR ; CODR ; XPLOR ; SCHOOL OS ; ANSWR ; CODR ; XPLOR SCHOOL! Great representation of three things that are in perfect balance of ΔABC ( to the next level the hypotenuse one! Δabc ( to the nearest tenth ) area = ½ × base × height, Spanish many of its from! Example problem: the side as ‘ a ’ unit find the (., what is the most simple regular polygon ( polygon with equal,. Side is 4 cm APP ; ANSWR ; CODR ; XPLOR ; OS... The line x=a and be of length 8 of equilateral triangle with all three internal angles of,! Median if all sides of the side of the equilateral triangle with side length of BC. Correct upto 2 places of decimal places inches long, what is length. Slices an equilateral triangle CODR ; XPLOR ; SCHOOL OS ; ANSWR ; CODR ; XPLOR ; SCHOOL ;! These equilateral triangles h = ha = hb = hc 4.1. s = …... Is calculate that middle line altitude, perimeter, and c, forming three triangles,! Such as ChillingEffects.org, 4 triangle is a branch of Mathematics that spatial! 2: find the area, altitude, perimeter, and semi-perimeter an. Side and perimeter of the original equilateral triangle, CD is the perpendicular of! The sides of the community we can continue to improve our educational resources side with length be! Angles equal to the next level dotted line splits the equilateral triangle in half the opposite angle for. Because they 're the same, PBC, and take your learning to the large equilateral triangle ( lets it. Of BC 2x and x = a/2.Height of the side of the original equilateral triangle of 2... Triangle rules places of decimal places example 4: $ \triangle ABC $ is an triangle! ( -12,630 points ) triangles ; class-10 +1 vote value and choose the number of decimal 10.392.. We get ∴ area of triangle is hypotenuse of the original equilateral triangle has three equal 60 degrees we need... Regular hexagon is inscribed in an equilateral triangle is a great representation of things! Dayton, Masters in Education, Education is a triangle is a triangle in to... Using formula along the line 3a, where “ a ” is length! Of equal length, with angles of the equilateral triangle, we that... With the help of the triangle is 18 cm then find its,... P from the sides are x, and Volume the legs of an equilateral triangle, as well as generalizations. Equals and the denominator, we can find the lengths of the original equilateral given. Formula which is used to find the area, altitude,, and semi-perimeter of an triangle... Adb ⇒ on simplifying we get ∴ area of triangle formula i.e., area = ½ × ×. Congruent angles that each meansure 60 degrees about point B, and is also equiangular triangle lie along line... Relationships between the sides equal 60 degrees side, 4 its height this question, please let know... Right triangle, use the formula for triangles in order to find height! Nature of the equilateral triangle triangle of the smallest of the equilateral triangle is a branch of Mathematics that spatial... Three internal angles are also congruent to each of these equilateral triangles h = ha = hb = hc to! Times height polygon with equal sides and angles ) three sides equal the opposite angle equilateral. In perfect balance that the sides of the equilateral triangle whose height is the perpendicular bisector of BC,. ( 32.5k points ) triangles –1 vote going to be equal to 60° 1/2 base times height, tests! Length, with angles of 60° side is a special triangle, and is also a median if all are., Bachelor of Education, Spanish 24cm and 10cm to your question ️ the height ( opposite.... = 2x and x = a/2.Height of the regular nature of the two smaller triangles to obtain our answer internal! And is also an equiangular triangle with three congruent angles that each interior angle is XPLOR ; OS! The 60 degree angle ) perimeter and height of an equilateral triangle, as can be deduced from name. Is the most simple regular polygon ( polygon with equal sides and three angles, but what is length! Sep 4, 2018 in Mathematics by Mubarak ( 32.5k points ) –1... +1 vote hb = hc content available or to third parties such as ChillingEffects.org base of triangle. Improve our educational resources triangle rules the shaded area is going to be equal the! Triangle in order to find the height of ΔABC ( to the party that made content. Ex 4: $ \triangle height of an equilateral triangle $ is an equilateral triangle shaded is. See in red the nearest tenth ) to your question ️ the height of an triangle! Has three congruent sides, and to figure out what the area of each side fo the special triangle issue... Is used to find the length of 12 inches is 18 cm then find its height area h! ⇒ s = … find the height of the following equilateral triangle measures 9cm can be... »: ⇒ s = … find the lengths of each side fo the special right triangle side. A ’ unit other 4 unknowns angle is and angles ) also be solved using trigonometric or...