Question

in the triangle shown, what is the value of x? a. $4.5sqrt{3}$ b. 9 c. $9sqrt{2}$ d. $9sqrt{3}$

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 60^{\circ}\), the opposite side is \(x\) and the hypotenuse is \(18\). So \(\sin60^{\circ}=\frac{x}{18}\).

Step2: Substitute the value of \(\sin60^{\circ}\)

Since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\), we have \(\frac{\sqrt{3}}{2}=\frac{x}{18}\).

Step3: Solve for \(x\)

Cross - multiply: \(x = 18\times\frac{\sqrt{3}}{2}\). Then \(x = 9\sqrt{3}\).

Answer:

D. \(9\sqrt{3}\)