1. Applications of Trigonometry
Lesson 14.5
Applications of Trigonometry pp

2. Objectives: 1. To apply trigonometric ratios to solve right triangles.
2. To apply trigonometry to solve word problems.

3. Definition
The angle of elevation is the angle formed by a horizontal line and the line of sight toward an object that is above the horizontal. The measure of this angle is the inclination.

4. line of sight
angle of elevation
horizontal

5. Definition
The angle of depression is the angle formed by a horizontal line and the line of sight toward an object that is below the horizontal. The measure of this angle is the declination.

6. horizontal
angle of depression
line of sight

7. Example 1
The KVLY-TV antenna near Blanchard, North Dakota, is the tallest structure in the world. Standing a distance of 1006 feet from the base of the antenna, you find the measure of the angle of elevation to the top of the antenna to be 64°. Find the height of the antenna.

8. Practice: A ramp is to be constructed with an angle of inclination of 15° that must reach the top of a 4-foot-high truck dock. How long is the incline of the ramp? x 4
15°

9. Practice: A ranger on a 260-foot-high lookout tower spots a forest fire at an angle of depression of 5°. How far away from the base of the tower is the fire? x 5°
260 y

10. Practice: A plane is traveling at an altitude of 3100 ft
Practice: A plane is traveling at an altitude of 3100 ft. A wind is blowing hard enough to cause a paratrooper to fall at an angle of 11° east of straight down. If he wants to land in a certain field, how far west of the field must he jump?

11. Homework pp

12. ►A. Exercises
1. A 40-foot guy wire is connected to a telephone pole, forming a 21° angle with the pole. How far from the pole is the guy wire anchored to the ground?
21°
40′ x
sin 21° = x 40
x = sin 21°(40)
≈ 14.3 ft.

13. ►A. Exercises
3. Dan finds the angle of depression from his location at the top of a mountain to a stream below to be 78°. The height of the mountain is 4830 feet above the stream. Find the horizontal distance from Dan to the stream.

14. ►A. Exercises
5. Karen has an exotic tropical bird that escaped from its cage. The bird is now on a tree branch 13 feet above the ground. If Karen places a 15-foot ladder against the tree branch, what angle does the ladder make with the ground?

15. ■ Cumulative Review
21. Give the measure of a central angle of a regular nonagon.

16. ■ Cumulative Review
22. Give the perimeter of a regular heptagon with a side of length 12.

17. ■ Cumulative Review
23. Give the area of a regular triangle with side of length 5.

18. ■ Cumulative Review
24. Give the area of a regular hexagon with side of length 5.

19. ■ Cumulative Review
25. Give the area of a regular octagon with side of length 6 and apothem of length