Question

Use the inverse of cosine to find the approximate measure of the missing angle. The hypotenuse is 65, the opposite is 33and the adjacent is 56.

30.5 degrees
43 degrees
59.5 degrees
90 degrees

Answer 1

To find the approximate measure of the missing angle using the given lengths of the sides in a right triangle, we can use the inverse cosine function.

Given:
- Opposite side = 33
- Adjacent side = 56

We will use the tangent function that relates the opposite and adjacent sides to find the angle θ:

\[
\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{33}{56}
\]

To find the angle θ, we use the inverse tangent (also called arctangent):

\[
\theta = \tan^{-1}\left(\frac{33}{56}\right)
\]

Calculating this:

\[
\frac{33}{56} \approx 0.5893
\]

Now, applying the inverse tangent:

\[
\theta \approx \tan^{-1}(0.5893)
\]

Using a calculator:

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

Thus, the measure of the missing angle is approximately **30.5 degrees**.