Question

A radio tower is located 300 feet from a building. From a window in the building, a person determines that the angle of elevation to the top of the tower is 21° and that the angle of depression to the bottom of the

tower is 20°. How tall is the tower?

Round your answer to 2 decimal places as needed.

Answer 1

We can use the tangent function to solve for the height of the tower. The tangent of an angle is the ratio of the opposite side to the adjacent side in a right triangle.

First, we'll find the opposite side (the height of the tower) using the angle of elevation:

tan(21°) = opposite / 300

opposite = 300 * tan(21°)

Then we'll find the opposite side (the depth of the base of the tower below the window) using the angle of depression:

tan(20°) = opposite / 300

opposite = 300 * tan(20°)

Now we can add the two opposite sides we found to get the total height of the tower

height = opposite(elevation) + opposite(depression)

height = 300 * tan(21°) + 300 * tan(20°)

The angle should be converted to radians before using the tangent function, and the final answer should be rounded to 2 decimal places.

Explanation: