Question

solve for x. round to the nearest tenth, if necessary. triangle with right angle at u, side ut = 64, angle at t is 70 degrees, side uv is x

Explanation:

Step1: Identify trigonometric ratio

In right triangle $UTV$, $\angle T=70^\circ$, opposite side to $\angle T$ is $x$, adjacent side is $64$. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(70^\circ)=\frac{x}{64}$

Step2: Solve for $x$

Rearrange to isolate $x$: $x=64\times\tan(70^\circ)$
Calculate $\tan(70^\circ)\approx2.747$, so $x\approx64\times2.747$

Step3: Compute final value

$x\approx64\times2.747=175.808$
Round to nearest tenth: $x\approx175.8$

Answer:

$175.8$