Question

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

Explanation:

Step1: Identify trigonometric relation

We use the sine function. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 48^{\circ}$ and the opposite side to the $48^{\circ}$ angle is 20, and the hypotenuse is $x$. So $\sin48^{\circ}=\frac{20}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{20}{\sin48^{\circ}}$. Since $\sin48^{\circ}\approx0.7431$, then $x=\frac{20}{0.7431}\approx26.9$.

Answer:

$26.9$