Question

find x. 9 3√3 6 6√3

Explanation:

Step1: Use trigonometric ratio

In a right - angled triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 30^{\circ}\), the opposite side is \(3\sqrt{3}\) and the adjacent side is \(x\).
\(\tan30^{\circ}=\frac{3\sqrt{3}}{x}\)

Step2: Substitute the value of \(\tan30^{\circ}\)

We know that \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\). So, \(\frac{1}{\sqrt{3}}=\frac{3\sqrt{3}}{x}\)

Step3: Cross - multiply

Cross - multiplying gives \(x = 3\sqrt{3}\times\sqrt{3}\)

Step4: Simplify the expression

\(x=3\times3=9\)

Answer:

\(9\)