Question

the longer leg of a 30°-60°-90° triangle is 9 millimeters long. how long is the shorter leg? write your answer in simplest radical form. millimeters

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a 30°-60°-90° triangle, the longer leg (opposite 60°) is $\sqrt{3}$ times the shorter leg (opposite 30°). Let $x$ = shorter leg, longer leg = $x\sqrt{3}$.

Step2: Set up equation and solve for $x$

Set $x\sqrt{3}=9$. Isolate $x$:
$$x=\frac{9}{\sqrt{3}}$$
Rationalize the denominator:
$$x=\frac{9\sqrt{3}}{\sqrt{3}\times\sqrt{3}}=\frac{9\sqrt{3}}{3}=3\sqrt{3}$$

Answer:

$3\sqrt{3}$ millimeters