Question

1. x = _ y = _

Explanation:

Step1: Use trigonometric ratios

For a right - triangle with angle \(60^{\circ}\), \(\tan60^{\circ}=\frac{\text{opposite}}{\text{adjacent}}=\frac{11\sqrt{3}}{x}\), and \(\cos60^{\circ}=\frac{\text{adjacent}}{\text{hypotenuse}}=\frac{x}{y}\).
Since \(\tan60^{\circ}=\sqrt{3}\), we have \(\sqrt{3}=\frac{11\sqrt{3}}{x}\).

Step2: Solve for \(x\)

Cross - multiply: \(\sqrt{3}x = 11\sqrt{3}\). Divide both sides by \(\sqrt{3}\), \(x = 11\).

Step3: Solve for \(y\)

Since \(\cos60^{\circ}=\frac{1}{2}\) and \(\cos60^{\circ}=\frac{x}{y}\) (with \(x = 11\)), then \(\frac{1}{2}=\frac{11}{y}\). Cross - multiply: \(y=22\).

Answer:

\(x = 11\), \(y = 22\)