Question

this is a 30 - 60 - 90 triangle. what is the measure of x? x = ?

Explanation:

Step1: Identify side ratios in 30-60-90 triangle

In a 30-60-90 triangle, the sides opposite 30°, 60°, 90° are in ratio $1:\sqrt{3}:2$. The side of length $\sqrt{3}$ is opposite 60°, so it corresponds to $\sqrt{3}$ in the ratio.

Step2: Find the side opposite 30°

The side opposite 30° is $1$ in the ratio, so it is $\frac{\sqrt{3}}{\sqrt{3}} = 1$.

Step3: Calculate x (side opposite 90°)

The hypotenuse (opposite 90°) is twice the side opposite 30°, so $x = 2 \times 1 = 2$.

Answer:

2