Question

find the missing side. round to the nearest tenth.
x
72°
6
x=

Explanation:

Step1: Identify the trigonometric ratio

We know the adjacent side to the angle and want to find the hypotenuse. Use cosine. $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 72^{\circ}$ and adjacent side $a = 6$, and hypotenuse is $x$. So, $\cos(72^{\circ})=\frac{6}{x}$.

Step2: Solve for $x$

We can re - arrange the equation to $x=\frac{6}{\cos(72^{\circ})}$. Since $\cos(72^{\circ})\approx0.309$, then $x=\frac{6}{0.309}\approx19.4$.

Answer:

$19.4$