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, the hypotenuse $c = 18$ and $x$ is the side opposite the 30 - degree angle.

Step2: Calculate the value of $x$

Since the side opposite the 30 - degree angle is half of the hypotenuse in a 30 - 60 - 90 triangle, we have $x=\frac{c}{2}$. Substituting $c = 18$ into the formula, we get $x=\frac{18}{2}$.

Answer:

$9$