1. LT 8.4: Solve Problems Involving Angles of Elevation and Depression

2. Math Humor Q: Why do mathematicians like the beach?
A: Because they have to sine and cosine to get a tan.

3. Discuss this picture with your group.
Pilots use the angles of elevation and depression to find most of the measurements they need to fly the plane.
Discuss this picture with your group.
What observations can you make about the angles of elevation and depression?
What information will we need to find:
m<2?
How high the plane is flying?
The horizontal distance the plane is from the tower?

4. If m<2=59º and TP = 17,500 ft, can you find how high the plane is flying to the nearest foot?
15000 feet

5. An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line. In the diagram, 1 is the angle of elevation from the tower T to the plane P.
An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line. 2 is the angle of depression from the plane to the tower.

6. Example 1:
Use the diagram above to classify each angle as an angle of elevation or angle of depression.
1a. 5
1b. 6

7. Since horizontal lines are parallel, 1  2 by the Alternate Interior Angles Theorem. Therefore the angle of elevation from one point is congruent
to the angle of depression from the other point.

8. Example 2:
Suppose a plane is at an altitude of 3500 ft and the angle of elevation from the airport to the plane is 29°. What is the horizontal distance between the plane and the airport? Round to the nearest foot.
6314 feet

9. Example 3:
A forest ranger in a 90-foot observation tower sees a fire. The angle of depression to the fire is 3°. What is the horizontal distance to this fire? Round to the nearest foot.
1717 feet 3°

10. Example 4:
A pilot flying at an altitude of 12,000 ft sights two airports directly in front of him. The angle of depression to one airport is 78°, and the angle of depression to the second airport is 19°. What is the distance between the two airports? Round to the nearest foot.
draw the picture for this diagram.

11. Example 4:
A pilot flying at an altitude of 12,000 ft sights two airports directly in front of him. The angle of depression to one airport is 78°, and the angle of depression to the second airport is 19°. What is the distance between the two airports? Round to the nearest foot.
78°
19°
12,000 ft
Make a plan with your group to solve the problem.

12. Example 4:
A pilot flying at an altitude of 12,000 ft sights two airports directly in front of him. The angle of depression to one airport is 78°, and the angle of depression to the second airport is 19°. What is the distance between the two airports? Round to the nearest foot.
CA = ft CB = ft
AB = ft
78°
19°
12,000 ft