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25 March, 06:21

A lifeguard on the shore in a chair that is 6 ft above the ground. She sees a swimmer at an angle of depression of 10°. About how far away from shore is the swimmer? Round your answer to the answer to the nearest foot.

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  1. 25 March, 07:39
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    34 ft

    Step-by-step explanation:

    The mnemonic SOH CAH TOA reminds you of the relationship between adjacent and opposite sides of a right triangle and the trig function of the associated angle. Here, the relevant relation is ...

    Tan = Opposite/Adjacent

    tan (10°) = (height of lifeguard) / (distance from shore)

    Then the distance from shore is ...

    distance from shore = (height of lifeguard) / tan (10°) ≈ (6 ft) / (0.17633)

    distance from shore ≈ 34 ft
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