Question

value: 2
solve for x. round to the nearest hundredth if necessary.
20
55°
x
a. 16.38
b. 28.56
c. 11.47
d. 34.87

Explanation:

Step1: Identify trigonometric ratio

We know that in a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 55^{\circ}$, the adjacent side to the angle $55^{\circ}$ is $x$ and the hypotenuse is 20. 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