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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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sqdancefan

Answer:

  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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