Question

Use the inverse of cosine to find the approximate measure of the missing angle  θ . (1 point) hypotenuse 65 adjacent 56

Answer 1

To find the angle \( \theta \) using the cosine function, you can use the following formula:

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

In your case, the adjacent side is 56 and the hypotenuse is 65. Plugging these values into the formula gives:

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

Now, use the inverse cosine function (also denoted as \( \cos^{-1} \) or \( \arccos \)) to find \( \theta \):

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

Calculating this value:

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

Now, we find \( \theta \):

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

Using a calculator:

\[
\theta \approx 30.1^\circ
\]

Thus, the approximate measure of the angle \( \theta \) is \( 30.1^\circ \).