Question

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

Explanation:

Step1: Use tangent function

In right - triangle $\triangle YXT$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 20^{\circ}$, the opposite side to the $20^{\circ}$ angle is $x$ and the adjacent side is $40$. So $\tan(20^{\circ})=\frac{x}{40}$.

Step2: Solve for $x$

Multiply both sides of the equation $\tan(20^{\circ})=\frac{x}{40}$ by $40$. We get $x = 40\times\tan(20^{\circ})$.
Since $\tan(20^{\circ})\approx0.364$, then $x = 40\times0.364 = 14.56$.

Step3: Round to the nearest tenth

Rounding $14.56$ to the nearest tenth gives $x\approx14.6$.

Answer:

$14.6$