Reed is snorkeling when he spots a stingray resting on the bottom of the ocean floor. He is on the surface of the water looking down. The water is 22 feet deep and the diagonal distance from him to the fish is 34 feet. Use the inverse of cosine to find the approximate angle of elevation with which he is looking at the fish. (1 point)

To find the angle of elevation from Reed to the stingray, we can use the cosine function in relation to the triangle formed by Reed, the stingray, and the point on the surface of the water directly above the stingray.

Let:

• \( d \) = diagonal distance from Reed to the stingray = 34 feet
• \( h \) = depth of the water = 22 feet
• \( \theta \) = angle of elevation from Reed to the stingray

We use the cosine function, which is defined as:

\[ \cos(\theta) = \frac{\text{adjacent side}}{\text{hypotenuse}} \]

In this case, the adjacent side is the depth of the water (22 feet) and the hypotenuse is the diagonal distance (34 feet):

\[ \cos(\theta) = \frac{22}{34} \]

Calculating that gives:

\[ \cos(\theta) = \frac{22}{34} \approx 0.6471 \]

Now, to find the angle \( \theta \), we use the inverse cosine function:

\[ \theta = \cos^{-1}(0.6471) \]

Using a calculator, we find:

\[ \theta \approx 49.5^\circ \]

Rounding this to the nearest degree gives approximately \( 50^\circ \).

Thus, the approximate angle of elevation with which Reed is looking at the fish is:

50°.