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Name: ____________________________________ Date: __________________ Using Trigonometry to Solve for Missing Sides Algebra 1 Right triangle trigonometry was developed in order to find missing sides of right triangles, similar to the Pythagorean Theorem. The key difference, though, is that with trigonometry as long as you have one side of a right triangle and one of the acute angles, you can then find the other two missing sides. TRIGONOMETRIC RATIOS Recall that in a right triangle with acute angle A, the following ratios are defined: sin A = opposite hypotenuse cos A = adjacent tan A = hypotenuse Exercise #1: For the right triangle below it is known that sin A = opposite adjacent 3 . Find the value of x. 4 20 x A Exercise #2: In the right triangle below, find the length of AB to the nearest tenth. C 26 38 B A The key in all of these problems is to properly identify the correct trigonometric ratio to use. Exercise #3: For the right triangle below, find the length of BC to the nearest tenth. B 65 A Algebra 1, Unit #8 – Right Triangle Trigonometry – L5 The Arlington Algebra Project, LaGrangeville, NY 12540 12 C Exercise #4: In each triangle below, use the appropriate trig function to solve for the value of x. Round to the nearest tenth. Triangles are not drawn to scale. (a) (b) 50 x 15 42 x 8 Exercise #5: Which of the following would give the length of BC shown below? (1) 18sin ( 34 ) (3) C 18 cos ( 34 ) 18 (2) 18 sin ( 34 ) (4) 18 tan ( 34 ) 34 A B Exercise #6: A ladder leans against a building as shown in the picture below. The ladder makes an acute angle with the ground of 72°. If the ladder is 14 feet long, how high, h, does the ladder reach up the wall? Round your answer to the nearest tenth of a foot. 14 feet h 72 Algebra 1, Unit #8 – Right Triangle Trigonometry – L5 The Arlington Algebra Project, LaGrangeville, NY 12540 Name: ____________________________________ Date: __________________ Using Trigonometry to Solve for Missing Sides Algebra 1 Homework Skill In problems 1 through 3, determine the trigonometric ratio needed to solve for the missing side and then use this ratio to find the missing side. 1. In right triangle ABC, m∠A = 58 and AB = 8 . Find the length of each of the following. Round your answers to the nearest tenth. C (a) BC (b) AC A 58 8 B 2. In right triangle ABC, m∠B = 44 and AB = 15 . Find the length of each of the following. Round your answers to the nearest tenth. (a) AC B 44 15 (b) BC C A 3. In right triangle ABC, m∠C = 32 and AB = 24 . Find the length of each of the following. Round your answers to the nearest tenth. B (a) AC 24 32 (b) BC Algebra 1, Unit #8 – Right Triangle Trigonometry – L5 The Arlington Algebra Project, LaGrangeville, NY 12540 C A 4. Which of the following would give the length of hypotenuse PR in the diagram below? (1) 8 cos ( 24 ) (2) 8 cos ( 24 ) (3) 8 tan ( 24 ) (4) R 8 tan ( 24 ) 24 Q 8 P Applications 5. An isosceles triangle has legs of length 16 and base angles that measure 48°. Find the height of the isosceles triangle to the nearest tenth. Hint – Create a right triangle by drawing the height. 16 16 48° 48° 6. Carlos walked 10 miles at an angle of 20 north of due east. To the nearest tenth of a mile, how far east, x, is Carlos from his starting point? N 10 miles 20 E x 7. Students are trying to determine the height of the flagpole at Arlington High. They have measured out a horizontal distance of 40 feet from the flagpole and site the top of it at an angle of elevation of 52 . What is the height, h, of the flagpole? Round your answer to the nearest tenth of a foot. h 52 Algebra 1, Unit #8 – Right Triangle Trigonometry – L5 The Arlington Algebra Project, LaGrangeville, NY 12540 40 ft