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 $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. In the right - triangle, $\theta = 55^{\circ}$, the hypotenuse is 20 and the side adjacent 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 $x=20\times0.5736 = 11.472$.

Step3: Round the result

Rounding $11.472$ to the nearest hundredth gives $x\approx11.47$.

Answer:

C. 11.47