Use the image to answer the question.

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

53°
53°

1°
1°

37°
37°

90°

Answer 1

To find the angle θ across from the side labeled 3 in the right triangle using the inverse cosine function, you can use the formula:

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

In this triangle, the adjacent side (the one next to angle θ) is 4, and the hypotenuse is 5. So we have:

\[ \cos(\theta) = \frac{4}{5} \]

Now, take the inverse cosine to find angle θ:

\[ \theta = \cos^{-1}\left(\frac{4}{5}\right) \]

Calculating this:

\[ \theta \approx 36.87° \]

Rounding to the nearest whole degree gives us:

\[ \theta \approx 37° \]

So the correct answer is:

37°