Question

Use the image to answer the question.

The hypotenuse of a right triangle is labeled 5 and the sides are labeled 3 and 4. The angle across from the side labeled 3 is labeled theta. A right angle symbol marks the right angle.

Use the inverse of cosine to solve for the missing angle, rounded to the nearest whole degree.

(1 point)
Responses

37°
37°

53°
53°

90°
90°

1°
1°
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Answer 1

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°**