Question

Use the image to answer the question.

The sides and angles of a triangle are labeled. The adjacent side is labeled 27, the hypotenuse is labeled 50, and the angle where the adjacent side and the hypotenuse meet is labeled with the theta symbol. The right angle is marked with a small box.

Use the inverse of cosine to find the indicated missing angle. Round your answer to the nearest tenth.

(1 point)
θ≈
°

Answer 1

To find the angle \( \theta \) using the inverse cosine function, we can use the adjacency and hypotenuse lengths given in the triangle.

The formula to find \( \theta \) in terms of cosine is:

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

In this triangle, the adjacent side is \( 27 \) and the hypotenuse is \( 50 \). Thus, we can substitute these values into the formula:

\[
\cos(\theta) = \frac{27}{50}
\]

Now we can find \( \theta \) using the inverse cosine (or arccos) function:

\[
\theta = \cos^{-1}\left(\frac{27}{50}\right)
\]

Calculating \( \frac{27}{50} \):

\[
\frac{27}{50} = 0.54
\]

Now, use a calculator to find \( \theta \):

\[
\theta = \cos^{-1}(0.54)
\]

Calculating this value, we get:

\[
\theta \approx 57.1° \text{ (rounded to the nearest tenth)}
\]

Thus, the answer is:

\[
\theta \approx 57.1°
\]