Question

1. find the missing variables.

3
60°
( x = )
( y = )

Explanation:

Step1: Use cosine to find \(x\)

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

Step2: Use tangent to find \(y\)

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 60^{\circ}\), adjacent side \( = 3\), opposite side \(=y\).
\(\tan60^{\circ}=\frac{y}{3}\)
Since \(\tan60^{\circ}=\sqrt{3}\), we have \(y = 3\sqrt{3}\).

Answer:

\(x = 6\), \(y = 3\sqrt{3}\)