Question

find the value of x.
(round to the nearest tenth as needed.)

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 57^{\circ}$, the adjacent side to the angle $57^{\circ}$ is 15 and the opposite side is $x$. So, $\tan(57^{\circ})=\frac{x}{15}$.

Step2: Solve for $x$

We know that $\tan(57^{\circ})\approx1.54$. Then $x = 15\times\tan(57^{\circ})$. Substituting the value of $\tan(57^{\circ})$, we get $x=15\times1.54 = 23.1$.

Answer:

$23.1$