Question

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

Explanation:

Step1: Use tangent function

In right - triangle $\triangle TWV$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 52^{\circ}$, the adjacent side to $\angle T$ is $96$ and the opposite side is $x$. So, $\tan(52^{\circ})=\frac{x}{96}$.

Step2: Solve for $x$

Multiply both sides of the equation by $96$: $x = 96\times\tan(52^{\circ})$.
Since $\tan(52^{\circ})\approx1.2799$, then $x=96\times1.2799 = 122.8704$.

Step3: Round to the nearest tenth

Rounding $122.8704$ to the nearest tenth gives $122.9$.

Answer:

$122.9$