Question

find the length of side x in simplest radical form with a rational denominator. answer attempt 1 out of 2 x=

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 triangle, if the side opposite the 30° angle is $a$, the side opposite the 60° angle is $a\sqrt{3}$, and the hypotenuse is $2a$. Here, the side opposite the 60° angle is $\sqrt{12}$, and the side opposite the 30° angle is $x$.

Step2: Set up the ratio equation

We know that $\frac{\text{side opposite 60°}}{\text{side opposite 30°}}=\sqrt{3}$. So $\frac{\sqrt{12}}{x}=\sqrt{3}$.

Step3: Solve for $x$

Cross - multiply to get $\sqrt{12}=\sqrt{3}x$. Then $x = \frac{\sqrt{12}}{\sqrt{3}}$. Simplify $\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}$. So $x=\frac{2\sqrt{3}}{\sqrt{3}} = 2$.

Answer:

$2$