Question

solve for ( x ). round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta=69^\circ$, opposite side to $\angle L$ is $36$, hypotenuse is $x$.

Step2: Rearrange to solve for $x$

$x=\frac{36}{\sin(69^\circ)}$

Step3: Calculate the value

First, $\sin(69^\circ)\approx0.9336$. Then $x\approx\frac{36}{0.9336}\approx38.6$

Answer:

$38.6$