Special right triangle is a triangle with some features that makes calculations easier and will yield exact answers. There are two types of special right triangles 45$^{0}$ - 45$^{0}$- 90$^{0}$ and 30$^{0}$ - 60$^{0}$ - 90$^{0}$.

1.

**30$^{0}$ - 60$^{0}$ - 90$^{0}$:** This right triangle has unique ratio of its sides and the ratio of the sides of a right angle triangle is 1: $\sqrt{3}$ : 2

Here the angles will be in arithmetic progression.

where H : Hypotenuse

LL : Long leg (Across from 60$^{0}$)

SL : Short leg (Across from 30$^{0}$)

The formula for short leg is

SL =

$\frac{1}{2}$ H

The formula for long leg is

LL =

$\frac{1}{2}$ H $\sqrt{3}$

Now combining the first two we get

LL = SL $\sqrt{3}$

2.

**45$^{0}$ - 45$^{0}$- 90$^{0}$:** In this triangle the angles will be in the ratio 1 : 1 : 2 and the sides are in the ratio 1 : 1 : $\sqrt{2}$.

**Isosceles Right Triangle**