Question

Find the measure of angle x. Round your answer to the nearest hundredth. (please type the numerical answer only) (4 points)

A right triangle is shown with one leg measuring 8 and another leg measuring 15. An angle across from the leg measuring 8 is marked x degrees.

Answer 1

To find the measure of angle x in the right triangle, we can use the tangent function, as it is defined as the ratio of the opposite side to the adjacent side.

Given:
- Opposite side = 8 (the side across from angle x)
- Adjacent side = 15 (the other leg)

We can use the tangent function:

\[
\tan(x) = \frac{\text{opposite}}{\text{adjacent}} = \frac{8}{15}
\]

To find angle x, take the arctangent (inverse tangent):

\[
x = \tan^{-1}\left(\frac{8}{15}\right)
\]

Now calculating that:

\[
x \approx \tan^{-1}\left(0.5333\right) \approx 28.07
\]

Rounding to the nearest hundredth:

28.07