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)

Responses

90°
90°

40°
40°

50°
50°

65°
65°

1 answer

To find the angle of elevation from Reed to the stingray, we can use the cosine function. The angle of elevation can be determined using the following relationship in a right triangle:

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

In this scenario:

  • The "adjacent" side is the depth of the water, which is 22 feet.
  • The "hypotenuse" is the diagonal distance from Reed to the stingray, which is 34 feet.

We can rearrange the equation to find the angle \(\theta\):

\[ \theta = \cos^{-1}\left(\frac{22}{34}\right) \]

Now, calculate \(\frac{22}{34}\):

\[ \frac{22}{34} = \frac{11}{17} \approx 0.6471 \]

Next, take the inverse cosine:

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

Using a calculator to find \(\theta\):

\[ \theta \approx 49.5° \]

Rounding this to the nearest degree gives approximately 50°. Therefore, the approximate angle of elevation with which Reed is looking at the fish is:

50°