question solve for x. round to the nearest tenth, if necessary.
question solve for x. round to the nearest tenth, if necessary.
Answer
Explanation:
Step1: Identify trigonometric relation
In right - triangle LMN, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 20^{\circ}$, the opposite side to $\theta$ is $52$ and the hypotenuse is $x$. So, $\sin20^{\circ}=\frac{52}{x}$.
Step2: Solve for $x$
We can rewrite the equation as $x=\frac{52}{\sin20^{\circ}}$. Since $\sin20^{\circ}\approx0.342$, then $x = \frac{52}{0.342}\approx152.0$.
Answer:
$152.0$