1. Angles of Elevation and Depression
Solve problems involving angles of elevation
Solve problems involving angles of depression
Aviators must fly at an angle of elevation to gain enough altitude to get over mountains.

2. Angles of Elevation
An Angle of Elevation is the angle between the line of sight and the horizontal when an observer looks upward.
Line of Sight
Angle of Elevation

3. Example
The angle of elevation of an airplane is 23°. If the airplane’s altitude is 2500 meters, how far away is it?
the distance to the airplane is the hypotenuse
the altitude of the airplane is the opposite side

4. Angles of Depression
An Angle of Depression is the angle between the line of sight and the horizontal when an observer looks downward.
Angle of Depression
Line of Sight

5. Angle of Depression
Line of Sight

7. Horizontal Line Horizontal Line Angle of Depression Angle of Elevation
55°
Angle of Depression
Angle of Elevation
Horizontal Line
55°

8. Example
You can walk across the Sydney Harbor Bridge and take a photo of the Opera House from about the same height as top of the highest sail.
This photo was taken from a point about 500 m horizontally from the Opera House and we observe the waterline below the highest sail as having an angle of depression of 8°. How high above sea level is the highest sail of the Opera House?

9. The angle of depression is 8°
The distance to the opera house is the adjacent side.
The height of the opera house is the opposite side.
The actual height is 67.4 meters

10. Lighthouse, Split Rock, Minnesota

11. Angle of Depression = 33°
195 ft.
Lighthouse, Split Rock, Minnesota

12. 33°
195 ft. d

13. Method 1 Use the alternate interior angle of elevation 195 ft. 33° d
The angle of elevation/depression is 33°
The height of the lighthouse is the opposite side
The distance to the boat is the adjacent side

14. Method 2 Use the complementary angle 57° 195 ft. d The angle is 57°
The height of the lighthouse is the adjacent side
The distance to the boat is the opposite side