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. Round your answer to the nearest tenth of a foot.

Answer 1

To find the distance from the base of the lifeguard's chair to the swimmer, we can use trigonometry and the given angle of depression. Using the tangent function, we find that the distance is approximately 15.36 feet.

Step-by-step explanation:

To find the distance from the base of the lifeguard's chair to the swimmer, we can use trigonometry and the given angle of depression. Let's call the distance we want to find 'x'.

Using the tangent function, we can write the equation tan(38°) = 12/x.

Solving for 'x', we have x = 12/tan(38°).

Using a calculator, we find that tan(38°) is approximately 0.7813.

Therefore, x = 12/0.7813 ≈ 15.36 feet.

So, the distance from the base of the lifeguard's chair to the swimmer is approximately 15.36 feet.