Question

Use the inverse of cosine to find the approximate measure of the missing angle θ.
Imagine a right triangle. The top line is labelled 56, the side line is labelled 33, and the slanted line on the left is labelled 65.
A. 90 degrees
B. 43 degrees
C. 30.5 degrees
D. 59.5 degrees

Answer 1

To find the missing angle \(\theta\) in the right triangle, you can use the cosine function. In a right triangle, the cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Here, it seems like we have the lengths:

- Adjacent side (top line) = 56
- Opposite side (side line) = 33
- Hypotenuse (slanted line) = 65

You can use the cosine function as follows:

\[
\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{56}{65}
\]

Now, use the inverse cosine function to find \(\theta\):

\[
\theta = \cos^{-1}\left(\frac{56}{65}\right)
\]

Calculating that:

1. First, calculate \(\frac{56}{65}\):

\[
\frac{56}{65} \approx 0.8615
\]

2. Now take the inverse cosine:

\[
\theta \approx \cos^{-1}(0.8615)
\]

Using a calculator:

\[
\theta \approx 30.5 \text{ degrees}
\]

Thus, the approximate measure of the missing angle \(\theta\) is:

**C. 30.5 degrees**