596 CHAPTER 8 Applications of Trigonometric Functions The Chapter Test Prep Videos include step-by-step solutions to all chapter test exercises. These videos are available in MyLab™ Math. 1. Find the exact value of the six trigonometric functions of the angle θ in the figure. u 3 6 2. Find the exact value of ° − ° sin40 cos50 . In Problems 3–5, use the given information to determine the three remaining parts of each triangle. 3. 528 C 17 a 19 B 4. 418 228 C 12 c b 5. C 8 10 5 A B In Problems 6–8, solve each triangle. 6. = ° = ° = A C a 55 , 20 , 4 7. = = = ° a b A 3, 7, 40 8. = = = ° a b C 8, 4, 70 9. Find the area of the triangle described in Problem 8. 10. Find the area of the triangle described in Problem 5. 11. A 12-foot ladder leans against a building. The top of the ladder leans against the wall 10.5 feet from the ground.What is the angle formed by the ground and the ladder? 12. A hot-air balloon is flying at a height of 600 feet and is directly above the Marshall Space Flight Center in Huntsville, Alabama. The pilot of the balloon looks down at the airport that is known to be 5 miles from the Marshall Space Flight Center. What is the angle of depression from the balloon to the airport? 13. Find the area of the shaded region enclosed in a semicircle of diameter 8 centimeters. The length of the chord AB is 6 centimeters. [Hint: Triangle ABC is a right triangle.] 6 B C A 8 14. Find the area of the quadrilateral shown. 728 11 8 7 5 15. Madison wants to swim across Lake William from the fishing lodge (point A) to the boat ramp (point B), but she wants to know the distance first. Highway 20 goes right past the boat ramp and County Road 3 goes to the lodge. The two roads intersect at point C, 4.2 miles from the ramp and 3.5 miles from the lodge. Madison uses a transit to measure the angle of intersection of the two roads to be ° 32 . How far will she need to swim? Hwy 20 4.2 miles CR 3 3.5 miles C A B Lake William 328 16. Given that ΔOAB is an isosceles triangle and the shaded sector is a semicircle, find the area of the entire region. Express your answer as a decimal rounded to two places. 408 O 5 B A 17. The area of the triangle shown below is 54 6 square units. Find the lengths of the sides. 7x 5x 6x 18. Logan is playing on her swing. One full swing (front to back to front) takes 6 seconds, and at the peak of her swing she is at an angle of ° 42 with the vertical. If her swing is 5 feet long, and we ignore all resistive forces, find a function that models her horizontal displacement (from the rest position) after time t. Chapter Test
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