Question

question solve for k and w.

Explanation:

Step1: Use sine function for w

We know that $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. In the right - triangle, for the $30^{\circ}$ angle, $\sin30^{\circ}=\frac{w}{5\sqrt{5}}$. Since $\sin30^{\circ}=\frac{1}{2}$, we have $\frac{w}{5\sqrt{5}}=\frac{1}{2}$.
$w = \frac{5\sqrt{5}}{2}$

Step2: Use cosine function for k

We know that $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For the $30^{\circ}$ angle, $\cos30^{\circ}=\frac{k}{5\sqrt{5}}$. Since $\cos30^{\circ}=\frac{\sqrt{3}}{2}$, we have $\frac{k}{5\sqrt{5}}=\frac{\sqrt{3}}{2}$.
$k=\frac{5\sqrt{15}}{2}$

Answer:

$w = \frac{5\sqrt{5}}{2}$, $k=\frac{5\sqrt{15}}{2}$