Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary.

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1 Name Homework Packet LESSON 7.6 For use with pages AND LESSON 7.7 For use with pages Find sin R and sin S. Then find cos R and cos S. Write each answer as a fraction and as a decimal. Round to four decimal places, if necessary. 1. sin R = = cos R = = sin S = = cos S = = 2. sin R = = cos R = = sin S = = cos S = = 3. sin R = = cos R = = sin S = = cos S = = Identify the side that is known with respect to the given angle. Next, choose a trig ratio which uses the known side. Set up and solve an equation using the appropriate ratio. Then find the other missing side using any method. Finally, find the other missing angle. Round all answers to the nearest tenth. 4. Know side (circle 1): Opposite Adjacent PQ = QR = m P = 5. Know side (circle 1): Opposite Adjacent UT = US = m U =

2 6. Know side (circle 1): Opposite Adjacent MD = DV = m V = 7. Know side (circle 1): Opposite Adjacent RT = TA = m T = 8. Know side (circle 1): Opposite Adjacent BC = AB = m C = 9. Know side (circle 1): Opposite Adjacent WV = WX = m V =

3 Let A be an acute angle in a right triangle. Approximate the measure of A to the nearest tenth of a degree. 10. sin A = tan A = sin A = cos A = tan A = cos A = sin A = cos A = tan A = 1 Identify the sides know with respect to angle A. Set up an equation using angle A and the appropriate ratio (sin, cos, or tan.) Find the measure of angle A by using the inverse relationship. Round to the nearest tenth of a degree. Then find the measure of angle B. 19. Known sides (circle 2): Opposite Adjacent 20. Known sides (circle 2): Opposite Adjacent 21. Known sides (circle 2): Opposite Adjacent

4 22. Known sides (circle 2): Opposite Adjacent Solve each triangle by finding all missing sides and angles. Show your work. 23. a = b = missing angle = 24. UT = U = S = 25. c = d = missing angle = 26. MN = N = M =

5 27. e = f = missing angle = 28. UM = U = E = 29. g = h = missing angle = 30. j = k = missing angle = 31. NP = P = N =

6 32. Staircase A staircase has an angle of elevation of 28 and covers a total distance of 17 feet. To the nearest foot, what is the vertical height h covered by the staircase? 33. Ladder You lean a 16 foot ladder against the wall. If the ladder makes an angle of 70 with the ground, how far away from the wall is the base of the ladder? Round your answer to the nearest tenth of a foot. 34. Suspension Bridge Use the diagram to find the distance across the suspension bridge. In Exercises 35 and 36, use the following information. Ramps The Uniform Federal Accessibility Standards specify that the ramp angle used for a wheelchair ramp must be less than or equal to The length of one ramp is 16 feet. The vertical rise is 14 inches. Estimate the ramp's horizontal distance and its ramp angle. Does this ramp meet the Uniform Federal Accessibility Standards? 36. You want to build a ramp with a vertical rise of 6 inches. You want to minimize the horizontal distance taken up by the ramp. Draw a sketch showing the approximate dimensions of your ramp.

Warm-Up Up Exercises. Use this diagram for Exercises If PR = 12 and m R = 19, find p. ANSWER If m P = 58 and r = 5, find p.

Warm-Up Up Exercises. Use this diagram for Exercises If PR = 12 and m R = 19, find p. ANSWER If m P = 58 and r = 5, find p. Warm-Up Up Exercises Use this diagram for Exercises 1 4. 1. If PR = 12 and m R = 19, find p. ANSWER 11.3 2. If m P = 58 and r = 5, find p. ANSWER 8.0 Warm-Up Up Exercises Use this diagram for Exercises