Question

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

Explanation:

Step1: Identify trigonometric relation

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In this right - triangle, $\theta = 33^{\circ}$, the opposite side to the $33^{\circ}$ angle is 9 and the hypotenuse is $x$. So, $\sin33^{\circ}=\frac{9}{x}$.

Step2: Solve for $x$

Cross - multiply to get $x\times\sin33^{\circ}=9$. Then $x = \frac{9}{\sin33^{\circ}}$.

Step3: Calculate the value of $x$

We know that $\sin33^{\circ}\approx0.5446$. So, $x=\frac{9}{0.5446}\approx16.5$.

Answer:

$16.5$