solve for x.\nx = (round to the nearest hundredth.)

Explanation:

Step1: Identify the trigonometric relation

In right - triangle ABC, we know the adjacent side to the angle $37^{\circ}$ is 23 and we want to find the opposite side $x$. We use the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan(37^{\circ})=\frac{x}{23}$.

Step2: Solve for $x$

Multiply both sides of the equation $\tan(37^{\circ})=\frac{x}{23}$ by 23. We get $x = 23\times\tan(37^{\circ})$. We know that $\tan(37^{\circ})\approx0.7536$. Then $x=23\times0.7536 = 17.3328$.

Step3: Round the result

Rounding 17.3328 to the nearest hundredth gives $x\approx17.33$.

Answer:

$17.33$