solve for $x$ in the triangle. round your answer to the nearest tenth. $x = \\square$

Explanation:

Step1: Identify trigonometric ratio

We have a right triangle, with the opposite side to the $42^\circ$ angle equal to 6, and $x$ is the hypotenuse. Use the sine function: $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

Step2: Substitute known values

$\sin(42^\circ) = \frac{6}{x}$

Step3: Rearrange to solve for $x$

$x = \frac{6}{\sin(42^\circ)}$

Step4: Calculate the value

First, $\sin(42^\circ) \approx 0.6691$, so $x \approx \frac{6}{0.6691} \approx 8.97$

Step5: Round to nearest tenth

Round 8.97 to the nearest tenth, which is 9.0

Answer:

$x = 9.0$