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?
1 answer:
Answer:
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 .
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