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

90°
90°

65°
65°

40°
40°

50°

Answer 1

To find the angle of elevation from Reed to the stingray, we can use the cosine function. We know the following:

• The depth of the water (adjacent side) = 22 feet
• The diagonal distance to the fish (hypotenuse) = 34 feet

We can use the cosine formula:

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

Substituting the values we have:

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

Now, we can calculate this value:

\[ \cos(\theta) = \frac{22}{34} = \frac{11}{17} \approx 0.6471 \]

Next, we find the angle \(\theta\) using the inverse cosine function \( \cos^{-1} \):

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

Using a calculator to find the angle:

\[ \theta \approx 49.5° \]

Rounding to the nearest degree, we get:

\[ \theta \approx 50° \]

So the approximate angle of elevation with which Reed is looking at the fish is 50°.