Question

d
10
60°
number
color
x=
y=

Explanation:

Step1: Use sine function for \(x\)

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 60^{\circ}\), hypotenuse \(= 10\), and the side opposite to \(60^{\circ}\) is \(x\).
\(\sin60^{\circ}=\frac{x}{10}\)
Since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\), we have \(\frac{\sqrt{3}}{2}=\frac{x}{10}\), then \(x = 10\times\frac{\sqrt{3}}{2}=5\sqrt{3}\)

Step2: Use cosine function for \(y\)

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 60^{\circ}\), hypotenuse \(= 10\), and the side adjacent to \(60^{\circ}\) is \(y\).
\(\cos60^{\circ}=\frac{y}{10}\)
Since \(\cos60^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{y}{10}\), then \(y = 10\times\frac{1}{2}=5\)

Answer:

\(x = 5\sqrt{3}\), \(y = 5\)