Question

solve for x in the triangle. round your answer to the nearest tenth.

Explanation:

Step1: Use sine - function definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 54^{\circ}$, the opposite side to the $54^{\circ}$ angle is $9$, and the hypotenuse is $x$. So, $\sin(54^{\circ})=\frac{9}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{9}{\sin(54^{\circ})}$. Since $\sin(54^{\circ})\approx0.809$, then $x = \frac{9}{0.809}\approx11.1$.

Answer:

$11.1$