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29 January, 16:48

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?

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  1. 29 January, 18:03
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    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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