# The hypotenuse of a 30-60-90 right triangle measure 18cm. What are the lengths of the longer leg and shorter leg?

Jul 4, 2015

The shorter leg is of length $9$cm.

The longer leg is of length $9 \sqrt{3}$cm $\cong 15.59$cm

#### Explanation:

A 30-60-90 triangle is one half of an equilateral triangle, so the shorter leg must be half as long as the hypotenuse.

Then using Pythagoras Theorem, the length of the longer leg in cm is given by:

length $= \sqrt{{18}^{2} - {9}^{2}} = \sqrt{3 \cdot {9}^{2}} = 9 \sqrt{3} \cong 15.59$

In general, the sides of a 30-60-90 triangle are in ratio $1 : \sqrt{3} : 2$.