Question

question solve for x and w. answer attempt 1 out of 3 x = w =

Explanation:

Step1: Use cosine function for x

$\cos(30^{\circ})=\frac{12\sqrt{6}}{x}$
Since $\cos(30^{\circ})=\frac{\sqrt{3}}{2}$, we have $\frac{\sqrt{3}}{2}=\frac{12\sqrt{6}}{x}$.
Cross - multiply: $x\times\sqrt{3}=2\times12\sqrt{6}$.
$x = \frac{24\sqrt{6}}{\sqrt{3}}$.
Rationalize the denominator: $x=\frac{24\sqrt{6}\times\sqrt{3}}{\sqrt{3}\times\sqrt{3}}=\frac{24\sqrt{18}}{3}=\frac{24\times3\sqrt{2}}{3}=24\sqrt{2}$.

Step2: Use sine function for w

$\sin(30^{\circ})=\frac{w}{x}$.
Since $\sin(30^{\circ})=\frac{1}{2}$ and $x = 24\sqrt{2}$, then $w=\frac{1}{2}\times24\sqrt{2}=12\sqrt{2}$.

Answer:

$x = 24\sqrt{2}$
$w=12\sqrt{2}$