Question

larissa dives into a pool that is 8 feet deep. she touches the bottom of the pool with her hands 6 feet horizontally from the point at which she entered the water. what is the approximate angle of elevation from the point on the bottom of the pool where she touched to her entry point? 36.9° 41.4° 48.6° 53.1°

Explanation:

Step1: Identify the sides of the right - triangle

The depth of the pool (opposite side to the angle of elevation) \(a = 8\) feet and the horizontal distance (adjacent side to the angle of elevation) \(b=6\) feet.

Step2: Use the tangent function

The tangent of an angle \(\theta\) in a right - triangle is given by \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan\theta=\frac{8}{6}=\frac{4}{3}\).

Step3: Find the angle \(\theta\)

Take the inverse tangent (arctan) of \(\frac{4}{3}\). \(\theta=\arctan(\frac{4}{3})\). Using a calculator, \(\theta\approx53.1^{\circ}\).

Answer:

\(53.1^{\circ}\)