Solving For Missing Angles Algebra 1
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1 Name: Solving For Missing ngles lgebra 1 Date: Today we will learn how to use right triangle trigonometry to find missing angles of a right triangle. In the first eercise, though, we will review how to solve for a missing side using trigonometry. Eercise #1: Find the length of to the nearest tenth Solving for a Missing ngle The process for finding a missing angle in a right triangle is very similar to that of finding a missing side. The key is to identify a trigonometric ratio that can be set up and then use the inverse trigonometric functions to solve for that angle. Eercise #2: Solve for m to the nearest degree. 3 5 Eercise #3: Find the value of, in the diagrams below, to the nearest degree. (a) (b) lgebra 1, Unit #8 Right Triangle Trigonometry L6 The rlington lgebra Project, LaGrangeville, NY 12540
2 Name: Skills Solving For Missing ngles lgebra 1 Homework Date: 1. For the following right triangles, find the measure of each angle,, to the nearest degree: (a) (b) (c) 21 (d) Given the following right triangle, which of the following is closest to m? (1) 28 (3) (2) 25 (4) In the diagram shown, m N is closest to M (1) 51 (3) 17 (2) 54 (4) P 21 N lgebra 1, Unit #8 Right Triangle Trigonometry L6 The rlington lgebra Project, LaGrangeville, NY 12540
3 Name: Skill Using Trigonometry to Solve for Missing Sides lgebra 1 Homework Date: 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, m = 58 and = 8. Find the length of each of the following. Round your answers to the nearest tenth. (a) (b) In right triangle, m = 44 and = 15. Find the length of each of the following. Round your answers to the nearest tenth. (a) (b) 3. In right triangle, m = 32 and = 24. Find the length of each of the following. Round your answers to the nearest tenth. (a) (b) lgebra 1, Unit #8 Right Triangle Trigonometry L5 The rlington lgebra Project, LaGrangeville, NY 12540
4 Eercise #4: Find the value of in the diagrams below. Round your answers to the nearest degree. (a) (b) Eercise #5: flagpole that is 45-feet high casts a shadow along the ground that is 52-feet long. What is the angle of elevation,, of the sun? Round your answer to the nearest degree. 45 feet 52 feet Eercise #6: hot air balloon hovers 75 feet above the ground. The balloon is tethered to the ground with a rope that is 125 feet long. t what angle of elevation, E, is the rope attached to the ground? Round your answer to the nearest degree. 125 feet 75 feet E lgebra 1, Unit #8 Right Triangle Trigonometry L6 The rlington lgebra Project, LaGrangeville, NY 12540
5 pplications 4. n isosceles triangle has legs measuring 9 feet and a base of 12 feet. Find the measure of the base angle,, to the nearest degree. (Remember: Right triangle trigonometry can only be used in right triangles.) skier is going down a slope that measures 7,500 feet long. y the end of the slope, the skier has dropped 2,200 vertical feet. To the nearest degree, what is the angle,, of the slope? 7,500 feet 2,200 feet Reasoning 6. ould the following triangle eist with the given measurements? Justify your answer lgebra 1, Unit #8 Right Triangle Trigonometry L6 The rlington lgebra Project, LaGrangeville, NY 12540
6 4. Which of the following would give the length of hypotenuse PR in the diagram below? (1) 8cos( 24 ) (3) 8tan( 24 ) R (2) 8 (4) cos( 24 ) 8 tan ( 24 ) Q 8 24 P pplications 5. n 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 reate a right triangle by drawing the height arlos walked 10 miles at an angle of 20 north of due east. To the nearest tenth of a mile, how far east,, is arlos from his starting point? N 10 miles 20 E 7. Students are trying to determine the height of the flagpole at rlington 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 lgebra 1, Unit #8 Right Triangle Trigonometry L5 The rlington lgebra Project, LaGrangeville, NY ft
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