Question

find the length of side x in simplest radical form with a rational denominator. answer attempt 1 out of 2 x =

Explanation:

Step1: Use cosine function

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\theta = 60^{\circ}$, the adjacent side to the $60^{\circ}$ angle is 2 and the hypotenuse is $x$. So, $\cos60^{\circ}=\frac{2}{x}$.
Since $\cos60^{\circ}=\frac{1}{2}$, we have the equation $\frac{1}{2}=\frac{2}{x}$.

Step2: Solve for $x$

Cross - multiply the equation $\frac{1}{2}=\frac{2}{x}$ to get $x\times1 = 2\times2$. So, $x = 4$.

Answer:

$4$