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 the tangent function since $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 37^{\circ}$, the opposite side to the angle is $x$ and the adjacent side is 22. So $\tan(37^{\circ})=\frac{x}{22}$.

Step2: Solve for x

We know that $\tan(37^{\circ})\approx0.7536$. Then $x = 22\times\tan(37^{\circ})$. Substituting the value of $\tan(37^{\circ})$, we get $x=22\times0.7536 = 16.5792\approx14.6$.

Answer:

$x\approx14.6$