Question

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

Explanation:

Step1: Use sine - function definition

In right - triangle $YTW$, $\sin W=\frac{opposite}{hypotenuse}$. Here, $\angle W = 31^{\circ}$, the opposite side to $\angle W$ is $x$ and the hypotenuse is $95$. So, $\sin31^{\circ}=\frac{x}{95}$.

Step2: Solve for $x$

Multiply both sides of the equation $\sin31^{\circ}=\frac{x}{95}$ by $95$. We know that $\sin31^{\circ}\approx0.515$. Then $x = 95\times\sin31^{\circ}$.
$x=95\times0.515 = 48.925$.

Step3: Round to the nearest tenth

Rounding $48.925$ to the nearest tenth gives $48.9$.

Answer:

$48.9$