Question

this is a 30 - 60 - 90 triangle. what is the measure of x? x 18 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 $c = 18$.

Step2: Set up proportion

Since $c = 2a$ in the 30 - 60 - 90 triangle ratio, and $c = 18$, we have $2x=18$.

Step3: Solve for $x$

Divide both sides of the equation $2x = 18$ by 2. So $x=\frac{18}{2}=9$.

Answer:

9