Question

find the measurement of the missing side indicated

Explanation:

Step1: Identify trigonometric relation

Assume the given side is adjacent to the $47^{\circ}$ angle and we want to find the opposite side. We use the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Let the adjacent side $a = 3$ and the angle $\theta = 47^{\circ}$, and the opposite side be $x$. So $\tan(47^{\circ})=\frac{x}{3}$.

Step2: Solve for $x$

We know that $\tan(47^{\circ})\approx1.0724$. Then $x = 3\times\tan(47^{\circ})\approx3\times1.0724 = 3.2172\approx3.21$.

Answer:

3.21