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Solving Right Triangles Table of Contents Solving Right Triangles .................................................................................................................................. 2 Problem 1: Solve Right Triangle - Solve a Triangle (Easy) ......................................................................... 4 Problem 2: Solve Right Triangle - Ladder against the Building (Easy)...................................................... 4 Problem 3: Solve Right Triangle - Determine Height of Tree (Easy) ......................................................... 5 Problem 4: Solve Right Triangle - Height of a Flagpole (Easy) .................................................................. 5 Answers ......................................................................................................................................................... 6 Trigonometry Page 1 Solving Right Triangles Solving Right Triangles Solving right triangles is a basic skill learned in Trigonometry. Solving a right triangle = determining the size of all three sides and all angles. These definitions will be needed to do that: Pythagorean equation: Where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. Trigonometry Page 2 Solving Right Triangles Example: John needs to determine the height of a flagpole. He determines the angle of elevation of the top of the pole to be 20° from a point on the ground 15 ft away from its base. a. Sketch the triangle. What are the angles? Find the height of the flagpole and hypotenuse. Solution: Flagpole 70 degrees c a 15 feet Tan 20o = a/15 (15)* Tan 20o = a 15 * .3640 = a 5.46 = a 20 degrees (elevation angle) height of flagpole Cos 20o = 15/c .9397 = 15/c .9397 * c = 15 c = 15/.9397 c = 15.96 length of hypotenuse Trigonometry Page 3 Solving Right Triangles Problem 1: Solve Right Triangle - Solve a Triangle (Easy) One angle of a right triangle measures 30 degrees and the hypotenuse has length 10. a. Determine the angles and sides of the triangle. Problem 2: Solve Right Triangle - Ladder against the Building (Easy) A ladder leans against a building. The ladder is 12 feet long. The ladder makes an angle of 60° with the ground. a. How far up the wall does the ladder reach? b. How far from the wall is the base of the ladder? Round your answers to two decimal places. Trigonometry Page 4 Solving Right Triangles Problem 3: Solve Right Triangle - Determine Height of Tree (Easy) Mary needs to determine the height of a tree. She measures the angle of elevation to be 30 degrees. Her distance from the base of the tree is 10 meters. a. How high is the tree to the nearest tenth of a meter? Problem 4: Solve Right Triangle - Height of a Flagpole (Easy) John needs to determine the height of a flagpole. He determines the angle of elevation to be 30° from a point on the ground 20 ft away from its base. b. Find the height of the flagpole. Trigonometry Page 5 Answers Solving Right Triangles 1a: angles = 30 degrees, 60 degrees, and 90 degrees. Sides = 8.66, 5, and the hypotenuse is 10 2a: 10.39 2b: 6.0 3a: 5.8 4a: 11.548 feet Trigonometry Page 6