Question

Solve for x. Round to the nearest tenth of a degree, if necessary. the hypotenuse is 78 the adjacent side is 54 and the angle is x

Answer 1

To find the angle \( x \) in a right triangle where the hypotenuse is \( 78 \) and the adjacent side is \( 54 \), we can use the cosine function:

\[
\cos(x) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{54}{78}
\]

First, calculate \( \frac{54}{78} \):

\[
\frac{54}{78} = \frac{27}{39} = \frac{9}{13} \approx 0.6923
\]

Now, we can find \( x \) by taking the arccosine (inverse cosine):

\[
x = \cos^{-1}\left(\frac{54}{78}\right) = \cos^{-1}\left(0.6923\right)
\]

Using a calculator:

\[
x \approx 46.6^\circ
\]

Thus, the value of \( x \), rounded to the nearest tenth of a degree, is:

\[
\boxed{46.6^\circ}
\]