Question

find a. 24 16 12 24√3

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 60^{\circ}\), the opposite side to \(60^{\circ}\) is \(12\sqrt{3}\) and the adjacent side is \(a\). So \(\tan60^{\circ}=\frac{12\sqrt{3}}{a}\).
Since \(\tan60^{\circ}=\sqrt{3}\), we have \(\sqrt{3}=\frac{12\sqrt{3}}{a}\).

Step2: Solve for \(a\)

Cross - multiply: \(\sqrt{3}\times a=12\sqrt{3}\).
Divide both sides by \(\sqrt{3}\): \(a = 12\).

Answer:

\(12\)