Question

c d 8 x y 30°

Explanation:

Step1: Find \(x\) using sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), opposite side \(= 8\), hypotenuse \(=x\).
\(\sin30^{\circ}=\frac{8}{x}\)
Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{8}{x}\).
Cross - multiply: \(x = 16\).

Step2: Find \(y\) using cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), adjacent side \(=y\), hypotenuse \(=x = 16\).
\(\cos30^{\circ}=\frac{y}{16}\)
Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), we have \(y = 16\times\frac{\sqrt{3}}{2}=8\sqrt{3}\).

Answer:

\(x = 16\), \(y = 8\sqrt{3}\)