Question

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

Explanation:

Step1: Identify trigonometric relation

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In right - triangle $BCD$, $\theta = 23^{\circ}$, the opposite side to $\theta$ is $CD = 9.5$ and the adjacent side is $BC=x$. So, $\tan23^{\circ}=\frac{9.5}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{9.5}{\tan23^{\circ}}$. Since $\tan23^{\circ}\approx0.4245$, then $x=\frac{9.5}{0.4245}\approx22.4$.

Answer:

$22.4$