# 10.7.4. Angles of Elevation and Angles of Depression

A body's angle of depression from the top of a 77-meter high tower is . Given that both the body and the tower's base are located on the same horizontal level, determine the distance between the body and the tower's base to the nearest meter.

• A154 meters
• B172 meters
• C86 meters
• D39 meters

### Example

A body's angle of depression from the top of a 77-meter high tower is . Given that both the body and the tower's base are located on the same horizontal level, determine the distance between the body and the tower's base to the nearest meter.

### Solution

In the following figure, is a right-angled triangle at .

The distance between the body and the tower's base is equal to . Also, since and are parallel line segments cut by transversal , the measure of is equal to . This means that in the figure above, . Use a calculator to determine the approximate length of as shown:

Thus, the distance between the tower and the body's base to the nearest metre is 154 metres.

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