1. Copyright © 2011 Pearson, Inc. 4.8 Solving Problems with Trigonometry

2. Copyright © 2011 Pearson, Inc. Slide 4.8 - 2 What you’ll learn about More Right Triangle Problems Simple Harmonic Motion … and why These problems illustrate some of the better- known applications of trigonometry.

3. Copyright © 2011 Pearson, Inc. Slide 4.8 - 3 Angle of Elevation, Angle of Depression An angle of elevation is the angle through which the eye moves up from horizontal to look at something above. An angle of depression is the angle through which the eye moves down from horizontal to look at something below.

4. Copyright © 2011 Pearson, Inc. Slide 4.8 - 4 Example Using Angle of Elevation The angle of elevation from the buoy to the top of the Barnegat Bay lighthouse 130 feet above the surface of the water is 5 º. Find the distance x from the base of the lighthouse to the buoy. 130 x 5º5º

5. Copyright © 2011 Pearson, Inc. Slide 4.8 - 5 Example Using Angle of Elevation The angle of elevation from the buoy to the top of the Barnegat Bay lighthouse 130 feet above the surface of the water is 5 º. Find the distance x from the base of the lighthouse to the buoy. 130 x 5º5º

6. Copyright © 2011 Pearson, Inc. Slide 4.8 - 6 Example Making Indirect Measurements From the top of a 100 ft. tall air traffic control tower, an airplane is observed flying toward the tower. If the angle of elevation of the airplane changes from 32º to 10º during the period of observation, and the altitude of the airplane changes from 500 ft to 200 ft, how far does the plane travel?

7. Copyright © 2011 Pearson, Inc. Slide 4.8 - 7 Example Making Indirect Measurements The figure models the situation.

8. Copyright © 2011 Pearson, Inc. Slide 4.8 - 8 Simple Harmonic Motion

9. Copyright © 2011 Pearson, Inc. Slide 4.8 - 9 Example Calculating Harmonic Motion A mass oscillating up and down on the bottom of a spring (assuming perfect elasticity and no friction or air resistance) can be modeled as harmonic motion. If the weight is displaced a maximum of 4 cm, find the modeling equation if it takes 3 seconds to complete one cycle.

10. Copyright © 2011 Pearson, Inc. Slide 4.8 - 10 Example Calculating Harmonic Motion

11. Copyright © 2011 Pearson, Inc. Slide 4.8 - 11 Quick Review 1. Solve for a. a 3 23 º

12. Copyright © 2011 Pearson, Inc. Slide 4.8 - 12 Quick Review

13. Copyright © 2011 Pearson, Inc. Slide 4.8 - 13 Quick Review Solutions 1. Solve for a. a 3 23 º

14. Copyright © 2011 Pearson, Inc. Slide 4.8 - 14 Quick Review Solutions

15. Copyright © 2011 Pearson, Inc. Slide 4.8 - 15 Chapter Test 5 C 12 α A B

16. Copyright © 2011 Pearson, Inc. Slide 4.8 - 16 Chapter Test

17. Copyright © 2011 Pearson, Inc. Slide 4.8 - 17 Chapter Test

18. Copyright © 2011 Pearson, Inc. Slide 4.8 - 18 Chapter Test Solutions 5 C 12 α A B

19. Copyright © 2011 Pearson, Inc. Slide 4.8 - 19 Chapter Test Solutions

20. Copyright © 2011 Pearson, Inc. Slide 4.8 - 20 Chapter Test Solutions

21. Copyright © 2011 Pearson, Inc. Slide 4.8 - 21 Chapter Test Solutions