Question

the longer leg of a 30°-60°-90° triangle has a length of 3√6 inches. what is the length of the hypotenuse? write your answer in simplest radical form. inches

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a 30°-60°-90° triangle, the longer leg (opposite 60°) is $\frac{\sqrt{3}}{2}$ times the hypotenuse $c$. So:
$\text{Longer leg} = \frac{\sqrt{3}}{2}c$

Step2: Substitute given leg length

Set $\frac{\sqrt{3}}{2}c = 3\sqrt{6}$

Step3: Solve for hypotenuse $c$

Rearrange to isolate $c$:
$c = 3\sqrt{6} \times \frac{2}{\sqrt{3}}$
Simplify $\frac{\sqrt{6}}{\sqrt{3}} = \sqrt{2}$, so:
$c = 3 \times 2 \times \sqrt{2} = 6\sqrt{2}$

Answer:

$6\sqrt{2}$ inches