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.

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