find the value of x. provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify trigonometric relation

We use the sine - function since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In the right - triangle, $\theta = 31^{\circ}$, the opposite side to the $31^{\circ}$ angle is $x$ and the hypotenuse is 43. So $\sin31^{\circ}=\frac{x}{43}$.

Step2: Solve for x

Multiply both sides of the equation $\sin31^{\circ}=\frac{x}{43}$ by 43. We know that $\sin31^{\circ}\approx0.515$. Then $x = 43\times\sin31^{\circ}$. $x=43\times0.515 = 22.145$.

Step3: Round to the nearest tenth

Rounding 22.145 to the nearest tenth gives $x\approx22.1$.

Answer:

$22.1$