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)

Question

Responses

40°
40°

65°
65°

50°
50°

90°
90°

Answer 1

To find the angle of elevation with which Reed is looking at the stingray, we can use the cosine function in the context of a right triangle formed by his line of sight, the water's surface, and the vertical depth of the water.

1. Let \( h \) be the depth of the water, which is 22 feet.
2. Let \( d \) be the diagonal distance from Reed to the fish, which is 34 feet.

Using the cosine formula, we have:

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

Substituting the known values:

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

Calculating the right side:

\[ \frac{22}{34} \approx 0.6471 \]

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

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

Calculating this using a calculator:

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

Rounding to the nearest whole number, we find:

\[ \theta \approx 50^\circ \]

Thus, the approximate angle of elevation is 50°.