To determine the height of a television tower, a person stands 135 ft from its base and determines the angle of elevation to the top of the tower to be 38 degrees. What is the height of the tower?

105.5 ft

Step-by-step explanation:

The tangent ratio is the ratio of the side opposite an angle to the adjacent side in a right triangle. Here, the side opposite the angle is the tower height, and the adjacent side is the distance to the tower. Then the appropriate relationship is ...

tan (38°) = (tower height) / (135 ft)

Multiplying by the denominator gives ...

tower height = (135 ft) ·tan (38°) ≈ 105.473 ft

The height of the tower is about 105.5 feet.