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.

Answer 1

To find the angle \( \theta \) in a right triangle using the cosine function, we can use the formula:

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

In your triangle:

- The adjacent side to angle \( \theta \) is 33.
- The hypotenuse is 65.

Now, we can calculate \( \cos(\theta) \):

\[
\cos(\theta) = \frac{33}{65}
\]

Next, we can find \( \theta \) by using the inverse cosine function:

\[
\theta = \cos^{-1}\left(\frac{33}{65}\right)
\]

Calculating \( \frac{33}{65} \):

\[
\frac{33}{65} \approx 0.5077
\]

Now, using a calculator or a cosine inverse function:

\[
\theta \approx \cos^{-1}(0.5077)
\]

When you calculate \( \theta \):

\[
\theta \approx 59.7^\circ
\]

Thus, the approximate measure of the missing angle \( \theta \) is about \( 59.7^\circ \).