Question

and drop the answers into the boxes! dark
x = 3
y = 3\sqrt{3}

Explanation:

Step1: Use cosine for \(x\)

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Given \(\theta = 60^{\circ}\) and hypotenuse \(c = 6\).
\(\cos60^{\circ}=\frac{x}{6}\)
Since \(\cos60^{\circ}=\frac{1}{2}\), we have \(x = 6\times\cos60^{\circ}=6\times\frac{1}{2}=3\)

Step2: Use sine for \(y\)

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Given \(\theta = 60^{\circ}\) and hypotenuse \(c = 6\).
\(\sin60^{\circ}=\frac{y}{6}\)
Since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\), we have \(y = 6\times\sin60^{\circ}=6\times\frac{\sqrt{3}}{2}=3\sqrt{3}\)

Answer:

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