Question

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

Explanation:

Step1: Use sine - cosine relationships

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$ and $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Given the angle of $30^{\circ}$, and the side of length $2$ opposite to the $30^{\circ}$ angle.
We know that $\sin30^{\circ}=\frac{2}{x}$. Since $\sin30^{\circ}=\frac{1}{2}$, we have the equation $\frac{1}{2}=\frac{2}{x}$.

Step2: Solve for $x$

Cross - multiply the equation $\frac{1}{2}=\frac{2}{x}$:
$x = 4$.

Step3: Use cosine to find $W$

We know that $\cos30^{\circ}=\frac{W}{x}$. Since $x = 4$ and $\cos30^{\circ}=\frac{\sqrt{3}}{2}$, we substitute $x$ into the equation: $W=x\cos30^{\circ}$.
$W = 4\times\frac{\sqrt{3}}{2}=2\sqrt{3}$.

Answer:

$W = 2\sqrt{3}$
$x = 4$