Question

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

Explanation:

Step1: Identify the trigonometric ratio

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$ in a right - triangle. Here, $\theta = 40^{\circ}$, the opposite side to $\theta$ is $9$ and the adjacent side is $x$. So, $\tan40^{\circ}=\frac{9}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{9}{\tan40^{\circ}}$. Since $\tan40^{\circ}\approx0.8391$, then $x=\frac{9}{0.8391}\approx10.7$.

Answer:

$10.7$