Question

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

Explanation:

Step1: Identify the trigonometric relation

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In this right - triangle, $\theta = 77^{\circ}$, the adjacent side to the angle $77^{\circ}$ is 23 and the hypotenuse is $x$. So, $\cos(77^{\circ})=\frac{23}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{23}{\cos(77^{\circ})}$. Since $\cos(77^{\circ})\approx0.225$, then $x=\frac{23}{0.225}\approx102.2$.

Answer:

$102.2$