Question

1. find x round to the nearest tenth.

Explanation:

Step1: Identify the trigonometric relation

We know that $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. In the right - triangle, $\theta = 52^{\circ}$, the opposite side to the angle $\theta$ is 21 and the adjacent side is $x$. So, $\tan(52^{\circ})=\frac{21}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{21}{\tan(52^{\circ})}$. Since $\tan(52^{\circ})\approx1.2799$, then $x=\frac{21}{1.2799}\approx16.4$.

Answer:

16.4