Question

Solve for x. Round to the nearest tenth, if necessary. the hypotenuse is x the angle is 68 degrees and the opposite side is 77

Answer 1

To solve for \( x \), the hypotenuse, in a right triangle where the opposite side is \( 77 \) and the angle is \( 68^\circ \), you can use the sine function, which is defined as:

\[
\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}
\]

In this case, you have:

\[
\sin(68^\circ) = \frac{77}{x}
\]

To isolate \( x \), rearrange the equation:

\[
x = \frac{77}{\sin(68^\circ)}
\]

Now, calculate \( \sin(68^\circ) \):

\[
\sin(68^\circ) \approx 0.9272
\]

Now substitute this value back into the equation:

\[
x \approx \frac{77}{0.9272} \approx 83.0
\]

Thus, the hypotenuse \( x \) is approximately:

\[
\boxed{83.0}
\]