1. 8.5 Angles of Elevation and Depression
Then: You used similar triangles to measure distances indirectly.
Now:
1. Solve problems involving angles of elevation and depression.
2. Use angles of elevation and depression to find the distance between two objects.

2. Angle of elevation
Angle formed by a horizontal line and an observer’s line of sight to an object above the horizontal line.

3. Angle of Depression
Angle formed by a horizontal line and an observer’s line of sight to an object below the horizontal line.

4. Example of Definitions:
Name the angle of elevation and the angle of depression in each figure. a. b.

5. Example 1: Angle of Elevation
The angle of elevation from point A to the top of a hill is 49. If point A is 400 feet from the base of the hill, how high is the hill?

6. Example 1: Angle of Elevation
Find the angle of elevation of the sun when a 12.5 meter tall telephone pole casts an 18 meter long shadow.

7. Example 2: Angle of Depression
A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom.

8. Example 2: Angle of Depression
From the top of a 120 foot high tower, an air traffic controller observes an airplane on the runway at an angle of 19. How far from the base of the tower is the airplane?

9. Example 3: Use Two Angles of Elevation or Depression
To estimate the height of a garage, Jason sights the top of the garage at a 42 angle of elevation. He then steps back 20 feet and sites the top at a 10 angle. If Jason is 6 feet tall, how tall is the garage to the nearest foot?

10. Example 3a:
Solve for AC, then AB, then add in eye height. 1). Find mDCA and m DAC 2) Find AC:

11. Example 3a:
3. Find AB:
4. Find the height of the building

12. Example 3: Use Two Angles of Elevation or Depression
Susan stands on the ground and sights to the top of a steep cliff at a 60 angle of elevation. She then steps back 50 meters and sights to the top of the steep cliff at a 30 angle. If Susan is1.8 meters tall, how tall is the steep cliff to the nearest meter?

13. Example 3b:
Solve for the height of the cliff:

14. p. 583-587 #4-8 all, 10-20 evens, 28-32 all, 34-38 evens
8.5 Assignment
p #4-8 all, evens, all, evens