Question

solve for the side
set up an equation, then solve for x. be accurate to within one decimal.

Explanation:

Step1: Identify trigonometric relation

We use $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here $\theta = 61^{\circ}$, opposite side is $x$ and hypotenuse is 38. So $\sin61^{\circ}=\frac{x}{38}$.

Step2: Solve for $x$

$x = 38\times\sin61^{\circ}$. Since $\sin61^{\circ}\approx0.8746$, then $x=38\times0.8746\approx33.2$.

Answer:

$x\approx33.2$