Question

a right triangle with dimensions given in units is shown below. what is the value of x in units? 8√2 4√3 4√2 8√3

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 30^{\circ}\), the opposite side is \(8\) and the adjacent side is \(x\). So \(\tan30^{\circ}=\frac{8}{x}\).

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

We know that \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\). Then \(\frac{1}{\sqrt{3}}=\frac{8}{x}\).

Step3: Solve for \(x\)

Cross - multiply gives \(x = 8\sqrt{3}\).

Answer:

\(8\sqrt{3}\) (the fourth option)