Question

if the hypotenuse in the following 30° - 60° - 90° triangle has length 10 inches, what are the lengths of the two legs?

Explanation:

Step1: Set up equation for hypotenuse

In a 30 - 60 - 90 triangle, if the hypotenuse is $2x$ and it is given as 10 inches, we have $2x = 10$.

Step2: Solve for $x$

Dividing both sides of the equation $2x = 10$ by 2, we get $x=\frac{10}{2}=5$.

Step3: Find lengths of legs

The shorter leg is $x$. So its length is 5 inches. The longer leg is $\sqrt{3}x$. Substituting $x = 5$, we get $\sqrt{3}\times5 = 5\sqrt{3}$ inches.

Answer:

The lengths of the two legs are 5 inches and $5\sqrt{3}$ inches.