Question

Find the angle measurement. Round to the nearest tenth.

Hypotenuse =20
Adjacent =9

9
26.7
63.3
24.2

Answer 1

To find the angle measurement in a right triangle with the given hypotenuse and adjacent side, you can use the cosine function:

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

Given that the hypotenuse is 20 and the adjacent side is 9, we can set up the equation:

\[
\cos(\theta) = \frac{9}{20}
\]

Now, let's calculate \( \theta \):

1. Calculate \( \frac{9}{20} \):

\[
\frac{9}{20} = 0.45
\]

2. Now, take the inverse cosine (also known as arccos) to find the angle \( \theta \):

\[
\theta = \cos^{-1}(0.45)
\]

Using a calculator, we find:

\[
\theta \approx 63.3^\circ
\]

Thus, rounding to the nearest tenth, the angle measurement is **63.3 degrees**.