Question

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

Explanation:

Step1: Identify the triangle type and trigonometric ratio

This is a right triangle (since $\angle V$ is a right angle). We know the hypotenuse ($WU = 4.9$) and we need to find the adjacent side to the $32^\circ$ angle ($x = WV$). The cosine function relates the adjacent side and the hypotenuse: $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. So, $\cos(32^\circ)=\frac{x}{4.9}$.

Step2: Solve for $x$

Multiply both sides by $4.9$ to isolate $x$: $x = 4.9\times\cos(32^\circ)$. Calculate $\cos(32^\circ)\approx0.8480$. Then $x\approx4.9\times0.8480$.

Step3: Compute the product

$4.9\times0.8480 = 4.1552$. Round to the nearest tenth: $4.2$.

Answer:

$4.2$