Question

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

Explanation:

Step1: Identify the trigonometric relation

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 52^{\circ}$, the adjacent - side to the angle $\theta$ is 21, and the hypotenuse is $x$. So, $\cos(52^{\circ})=\frac{21}{x}$.

Step2: Solve for $x$

We can rewrite the equation as $x=\frac{21}{\cos(52^{\circ})}$. Since $\cos(52^{\circ})\approx0.6157$, then $x=\frac{21}{0.6157}\approx33.5$.

Answer:

33.5