Question

what is the value of $x$ in the figure shown? show calculator

Explanation:

Step1: Find \(\tan60^{\circ}\)

In \(\triangle ABC\), \(\tan60^{\circ}=\frac{AC}{AB}\). Let \(AC = x\), \(AB = 20\sqrt{3}\). Since \(\tan60^{\circ}=\sqrt{3}\), we have \(\sqrt{3}=\frac{x}{20\sqrt{3}}\).

Step2: Solve for \(x\)

Cross - multiply: \(x=\sqrt{3}\times20\sqrt{3}\). Using the rule \(a\sqrt{b}\times c\sqrt{d}=ac\sqrt{bd}\), here \(a = c = \sqrt{3}\), \(b = d = 3\). So \(x = 20\times3=60\).

Answer:

\(60\)