To find the angle of elevation (\(\theta\)) that Nathan is looking at the shark, we can use the cosine function, which is defined as:
\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \]
In this case:
- The adjacent side is the depth of the water, which is 15 feet.
- The hypotenuse is the diagonal distance to the shark, which is 42 feet.
Now we can set up the equation:
\[ \cos(\theta) = \frac{15}{42} \]
Next, we calculate \(\frac{15}{42}\):
\[ \frac{15}{42} = \frac{5}{14} \approx 0.3571 \]
Now we use the inverse cosine to find \(\theta\):
\[ \theta = \cos^{-1}\left(0.3571\right) \]
Using a calculator to find the angle:
\[ \theta \approx 69° \]
Therefore, the approximate angle of elevation which Nathan is looking at the shark is:
69°