Question

lanssa 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? 48.6° 36.9° 53.1° 41.4°

Explanation:

Step1: Identify right - triangle sides

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

Step2: Use tangent function

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

Step3: Find the angle

We know that $\theta=\arctan(\frac{4}{3})$. Using a calculator, $\theta\approx53.1^{\circ}$.

Answer:

$53.1^{\circ}$