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 is the answer 35.6?

Answer 1

To solve for \( x \) in a right triangle, where the angle is \( 66^\circ \), the opposite side is \( 80 \), and the adjacent side is \( x \), we can use the tangent function:

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

In this case:

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

To find \( x \), we can rearrange this equation:

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

Now, we need to calculate \( \tan(66^\circ) \). Using a calculator:

\[
\tan(66^\circ) \approx 2.576
\]

Now substituting this value back into the formula for \( x \):

\[
x \approx \frac{80}{2.576} \approx 31.0
\]

So, the value of \( x \) is approximately \( 31.0 \) when rounded to the nearest tenth.

Therefore, if you found an answer of \( 35.6 \), that is not correct based on these calculations. The correct rounded value for \( x \) is approximately \( 31.0 \).