Question

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

Answer 1

The shorter leg is of length `9`cm.

The longer leg is of length `9sqrt(3)`cm `~= 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*9^2) = 9sqrt(3) ~= 15.59`

In general, the sides of a 30-60-90 triangle are in ratio `1 : sqrt(3) : 2`.