Question

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

Explanation:

Step1: Use sine - rule in triangle

In right - triangle $\triangle YTW$, $\sin W=\frac{YT}{YW}$. Given $\angle W = 31^{\circ}$ and $YW = 95$, and $YT=x$.
We know that $\sin W=\sin31^{\circ}\approx0.515$.
The sine - rule formula is $\sin W=\frac{x}{95}$.

Step2: Solve for $x$

Cross - multiply the equation $\sin31^{\circ}=\frac{x}{95}$ to get $x = 95\times\sin31^{\circ}$.
Substitute $\sin31^{\circ}\approx0.515$ into the equation: $x=95\times0.515 = 48.925$.

Step3: Round to the nearest tenth

Rounding $48.925$ to the nearest tenth gives $x\approx48.9$.

Answer:

$48.9$