Question

find the missing side. round to the nearest tenth.
49°
14
x
x=

Explanation:

Step1: Identify the trigonometric ratio

We know the opposite side to the angle and want to find the adjacent side. We use the tangent function $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 49^{\circ}$ and the opposite side is 14, and the adjacent side is $x$. So $\tan49^{\circ}=\frac{14}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{14}{\tan49^{\circ}}$. Since $\tan49^{\circ}\approx1.150368$, then $x=\frac{14}{1.150368}\approx12.2$.

Answer:

$x\approx12.2$