Question

38√15 30° x

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 30^{\circ}\), the opposite side is \(x\) and the adjacent side is \(38\sqrt{15}\).
\(\tan30^{\circ}=\frac{x}{38\sqrt{15}}\)

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

Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), we have \(\frac{1}{\sqrt{3}}=\frac{x}{38\sqrt{15}}\)
Cross - multiply: \(x=\frac{38\sqrt{15}}{\sqrt{3}}\)

Step3: Simplify the expression

Rationalize the denominator: \(x = 38\sqrt{\frac{15}{3}}\)
\(x=38\sqrt{5}\)

Answer:

\(38\sqrt{5}\)