Question

x 45° 18√3

Explanation:

Step1: Use trigonometric ratio (tangent)

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 45^{\circ}\), the adjacent side is \(18\sqrt{3}\), and the opposite side is \(x\). So, \(\tan45^{\circ}=\frac{x}{18\sqrt{3}}\).

Step2: Substitute the value of \(\tan45^{\circ}\)

Since \(\tan45^{\circ}=1\), we have \(1=\frac{x}{18\sqrt{3}}\).

Step3: Solve for \(x\)

Multiply both sides by \(18\sqrt{3}\), so \(x = 18\sqrt{3}\).

Answer:

\(x = 18\sqrt{3}\)