Question

(Trig. Functions and Angles of Elevation & Depression)

A lifeguard is sitting on her tower 5 feet above the ground. She sees a swimmer in the pool beneath her stand when she looks downward at an angle of depression of 22°
. What is the horizontal distance between the swimmer and the base of the lifeguard's tower?

Answer 1

Answer: 12.1 feet

Explanation:

To solve the problem, we can use trigonometry and the tangent function.

Let's denote the horizontal distance between the swimmer and the base of the lifeguard's tower as x. We can draw a right triangle with the lifeguard's tower, the swimmer, and the horizontal distance x as its sides. The angle between the lifeguard's line of sight and the horizontal line passing through the base of the tower is 90 degrees since the line of sight is perpendicular to the ground. The angle of depression, which is the angle between the line of sight and the line passing through the swimmer and the base of the tower, is 22 degrees.

Using the tangent function, we can write:

tan(22) = 5/x

Solving for x, we get:

x = 5/tan(22) ≈ 12.1 feet

Therefore, the horizontal distance between the swimmer and the base of the lifeguard's tower is approximately 12.1 feet.