Question

find the length of side ( x ) to the nearest tenth.

Explanation:

Step1: Identify right triangle ratios

In a right triangle, $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta=30^\circ$, opposite side is $\sqrt{10}$, hypotenuse is $x$.

Step2: Rearrange to solve for $x$

Rearrange the sine formula: $x=\frac{\sqrt{10}}{\sin(30^\circ)}$. Since $\sin(30^\circ)=\frac{1}{2}$, substitute:
$x=\frac{\sqrt{10}}{\frac{1}{2}}=2\sqrt{10}$

Step3: Calculate decimal value

Compute $2\sqrt{10}\approx2\times3.1623=6.3246$, round to nearest tenth.

Answer:

6.3