Question

solve for x. round to the nearest hundredth if necessary. 20 55° x

Explanation:

Step1: Identify trigonometric ratio

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 55^{\circ}$, the hypotenuse is 20 and the adjacent side to the $55^{\circ}$ angle is $x$. So, $\cos(55^{\circ})=\frac{x}{20}$.

Step2: Solve for $x$

Multiply both sides of the equation $\cos(55^{\circ})=\frac{x}{20}$ by 20. We get $x = 20\times\cos(55^{\circ})$.
Since $\cos(55^{\circ})\approx0.5736$, then $x=20\times0.5736 = 11.472\approx11.47$.

Answer:

C. 11.47