Question

Solve for x. Round to the nearest tenth, if necessary. the angle is 66 degrees and the opposite side is 80 the adjacent side is x

Answer 1

To solve for \( x \) in a right triangle where you have the angle \( \theta = 66^\circ \), the opposite side \( O = 80 \), and you're looking for the adjacent side \( A = x \), you can use the tangent function, which is defined as:

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

Substituting the known values:

\[
\tan(66^\circ) = \frac{80}{x}
\]

Now, rearranging the equation to solve for \( x \):

\[
x = \frac{80}{\tan(66^\circ)}
\]

Next, we will calculate \( \tan(66^\circ) \). Using a calculator:

\[
\tan(66^\circ) \approx 2.578
\]

Now substitute this back into the equation for \( x \):

\[
x = \frac{80}{2.578} \approx 31.0
\]

Therefore, rounding to the nearest tenth, the length of the adjacent side \( x \) is approximately:

\[
\boxed{31.0}
\]