Angles of Elevation and Depression

Solve problems involving angles of elevation and angles of depression.

Unit J 2

Angles of Elevation and Depression

An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line.

An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line.

Unit J 3

Angles of Elevation and Depression

Angle of depression

Angle of elevation

Unit J 4

Example: Angle of Elevation

If we know the height of the lighthouse above sea level and the angle of elevation, we can find the distance from the boat to the shore.

200tan 15

x.

2000.2679

x

..746.5 ft. x200 0.2679 x

In this case, the top of the light-house is 200 feet above sea level, and the angle of elevation is 15°.

200 ft.

15° x

Unit J 5

Key Concepts – Get Organized

Angle of Elevation

Words

An angle formed by a horizontal line and a line of sight to a point above.

Diagram

Unit J 6

Key Concepts – Get Organized

Angle of Depression

Words

An angle formed by a horizontal line and a line of sight to a point below.

Diagram

Unit J 7

Lesson Quiz – Part I

Using the diagram, name each angle type:

1. ∠1

2. ∠2

3. ∠3

4. ∠4

angle of elevation

angle of depression

angle of depression

angle of elevation

Unit J 8

Lesson Quiz – Part II5. A person snorkeling sees a turtle on the ocean

floor at an angle of depression of 38º. She is 14 feet above the ocean floor. How far from the turtle is she? Round to the nearest foot.

38°

This angle is also 38°. We will use the sin 38°, since we have the opposite leg and need to find the hypotenuse.

14

sin 38.x

14

0.6157x→

23x 22.7 .ft.