Question

question solve for w and k.

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 hypotenuse $c = 8$, for the $30^{\circ}$ angle, if the side opposite the $30^{\circ}$ angle is $k$ and the side adjacent is $w$.
We know that $\sin30^{\circ}=\frac{k}{8}$. Since $\sin30^{\circ}=\frac{1}{2}$, we have $k = 8\times\sin30^{\circ}$.
$k=8\times\frac{1}{2}=4$.

Step2: Use cosine formula

We also know that $\cos30^{\circ}=\frac{w}{8}$. Since $\cos30^{\circ}=\frac{\sqrt{3}}{2}$, we have $w = 8\times\cos30^{\circ}$.
$w = 8\times\frac{\sqrt{3}}{2}=4\sqrt{3}$.

Answer:

$k = 4$, $w = 4\sqrt{3}$