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

2. Copyright © 2011 Pearson, Inc. Slide 4.8 - 2 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.

3. Copyright © 2011 Pearson, Inc. Slide 4.8 - 3 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

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 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?

6. Copyright © 2011 Pearson, Inc. Slide 4.8 - 6 Example Making Indirect Measurements The figure models the situation.

7. Copyright © 2011 Pearson, Inc. Slide 4.8 - 7 Chapter Test 5 C 12 α A B

8. Copyright © 2011 Pearson, Inc. Slide 4.8 - 8 Chapter Test

9. Copyright © 2011 Pearson, Inc. Slide 4.8 - 9 Chapter Test

10. Copyright © 2011 Pearson, Inc. Slide 4.8 - 10 Chapter Test Solutions 5 C 12 α A B

11. Copyright © 2011 Pearson, Inc. Slide 4.8 - 11 Chapter Test Solutions

12. Copyright © 2011 Pearson, Inc. Slide 4.8 - 12 Chapter Test Solutions

13. Copyright © 2011 Pearson, Inc. Slide 4.8 - 13 Chapter Test Solutions