Question

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

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 triangle, if the hypotenuse is $c$, the side opposite the 30 - degree angle is $a$, and the side opposite the 60 - degree angle is $b$, the ratio of the sides is $a:b:c = 1:\sqrt{3}:2$. Here, assume the side opposite the 30 - degree angle is $x$ and the hypotenuse is 10.

Step2: Set up proportion

Since the ratio of the side opposite 30 - degree angle to the hypotenuse is $\frac{1}{2}$, we have $\frac{x}{10}=\frac{1}{2}$ for the relationship between the side opposite 30 - degree angle and the hypotenuse. But if $x$ is the side opposite the 60 - degree angle, and the hypotenuse $c = 10$, and the ratio of the side opposite 60 - degree angle to the hypotenuse is $\frac{\sqrt{3}}{2}$. So $x=\frac{\sqrt{3}}{2}\times10 = 5\sqrt{3}$.

Answer:

$x = 5\sqrt{3}$