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 42° and that the angle of depression to the bottom of the tower is 37°. How tall is the tower?

Answer 1

Answer:

The tower is approximately 381 feet high.

Step-by-step explanation:

Refer to the sketch attached. The height of the tower can be found in two parts:

• The part above the window, and
• The part under the window.

Each part can be seen as a leg of a right triangle. The other leg is the distance between the building and the tower and is 300-feet long. The angle opposite to the leg is given.

• The length of the upper part is $300\cdot \sin{42^{\circ}}$ feet.
• The length of the lower part is $300\cdot \sin{37^{\circ}}$.

The height of the tower is the sum of the two parts:

$300\cdot \sin{42^{\circ}} + 300\cdot \sin{37^{\circ}} = 300(\sin{42^{\circ}}+\sin{37^{\circ}}) = 381$ feet.