Question

this is a 30 - 60 - 90 triangle. what is the measure of x? 4\sqrt{3} x = ?

Explanation:

Step1: Identify side ratios

In a 30-60-90 triangle, sides are in ratio $1:\sqrt{3}:2$ (opposite 30°, 60°, 90°).

Step2: Match given side to ratio

Assume $4\sqrt{3}$ is the longer leg (opposite 60°), so shorter leg = $\frac{4\sqrt{3}}{\sqrt{3}} = 4$.

Step3: Find hypotenuse

Hypotenuse = 2×shorter leg = $2×4 = 8$. (Assuming x is hypotenuse, common in such problems.)

Answer:

8