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

Explanation:

Step1: Identify trigonometric ratio

In right - triangle $\triangle WUV$, we know the hypotenuse $WU = 4.9$ and we want to find the adjacent side $x$ to the angle $\angle W=32^{\circ}$. We use the cosine function. $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, so $\cos(32^{\circ})=\frac{x}{4.9}$.

Step2: Solve for $x$

Multiply both sides of the equation $\cos(32^{\circ})=\frac{x}{4.9}$ by $4.9$. We get $x = 4.9\times\cos(32^{\circ})$. Since $\cos(32^{\circ})\approx0.848$, then $x = 4.9\times0.848=4.1552$.

Step3: Round the result

Rounding $4.1552$ to the nearest tenth, we get $x\approx4.2$.

Answer:

$4.2$