Question

The angle of depression from a lifeguard in her chair to a person swimming in a pool is 38 degrees. If the height of the chair is 12 feet tall, find the distance from the base of the lifeguard's chair to the swimmer.

Answer 1

15.36 feet

Explanation:

We solve the above question using Trigonometric function of Tangent

Tan θ = Opposite /Adjacent

From the question

θ = 38°

Opposite = the height of the chair = 12 feet tall

Adjacent = the distance from the base of the lifeguard's chair to the swimmer = x

Hence:

tan 38° = 12/x

Cross Multiply

tan 38° × x = 12

x = 12/tan 38°

x = 15.359299586

x ≈ 15.36 feet

Hence, the distance from the base of the lifeguard's chair to the swimmer is 15.36 feet