Nathan is snorkeling when he spots a shark on the bottom of the ocean floor. He is on the surface of the water looking down. The water is 15 feet deep and the diagonal distance from him to the shark is 42 feet. Use the inverse of cosine to find the approximate angle of elevation which he is looking at the shark.(1 point)

Question

Responses

20°
20°

69°
69°

45°
45°

21°

Answer 1

To find the angle of elevation from Nathan to the shark, we can use the cosine function. We know the adjacent side (the depth of the water) is 15 feet, and the hypotenuse (the diagonal distance from Nathan to the shark) is 42 feet.

The cosine of the angle of elevation \( \theta \) can be expressed as:

\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{15}{42} \]

Now, we can calculate \( \cos(\theta) \):

\[ \cos(\theta) = \frac{15}{42} \approx 0.3571 \]

Next, we find the angle \( \theta \) by taking the inverse cosine (arccos) of 0.3571:

\[ \theta = \cos^{-1}(0.3571) \]

Calculating this using a scientific calculator:

\[ \theta \approx 69.44° \]

Rounding it gives approximately 69°.

Thus, the angle of elevation at which Nathan is looking at the shark is approximately:

69°