Question

gina wilson (all things algebra)

Explanation:

Step1: Recall sine - ratio formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 24^{\circ}$, the opposite side to the angle $24^{\circ}$ is $x$ and the hypotenuse is $9$. So, $\sin(24^{\circ})=\frac{x}{9}$.

Step2: Solve for $x$

Cross - multiply the equation $\sin(24^{\circ})=\frac{x}{9}$ to get $x = 9\times\sin(24^{\circ})$. Using a calculator, $\sin(24^{\circ})\approx0.4067$, then $x=9\times0.4067 = 3.6603\approx3.7$.

Answer:

$x\approx3.7$