To find the angle \( \theta \) across from the side labeled 3 in the right triangle, we can use the cosine function. The cosine of an angle in a right triangle is defined as the ratio of the length of the adjacent side to the hypotenuse.
Given:
- Hypotenuse = 5
- Adjacent side (side next to angle \( \theta \)) = 4
- Opposite side (side across from angle \( \theta \)) = 3
We want to use the cosine of \( \theta \):
\[ \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{4}{5} \]
To find \( \theta \), we take the inverse cosine (arccos):
\[ \theta = \cos^{-1}\left(\frac{4}{5}\right) \]
Now we can calculate \( \theta \):
\[ \theta \approx \cos^{-1}(0.8) \]
Using a calculator:
\[ \theta \approx 36.87° \]
Rounded to the nearest whole degree, \( \theta \) is \( 37° \).
So, the correct response is:
37°