Question

solve for $x$. round to the nearest tenth, if necessary.
right triangle $uvw$ with right angle at $v$, angle at $u$ is $50^{\circ}$, side $wu = 6.1$, side $uv = x$

Explanation:

Step1: Identify adjacent side/hypotenuse

In right $\triangle UVW$, $\angle U=50^\circ$, hypotenuse $UW=6.1$, $x$ is adjacent to $\angle U$. Use cosine:
$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Substitute values and solve for $x$

$\cos(50^\circ)=\frac{x}{6.1}$
$x=6.1\times\cos(50^\circ)$
Calculate $\cos(50^\circ)\approx0.6428$, so:
$x\approx6.1\times0.6428$

Step3: Compute final value

$x\approx3.921$
Round to nearest tenth: $x\approx3.9$

Answer:

$3.9$