Special Right Triangles (30-60-90 & 45-45-90)

A special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1 : @@rac{{ ext{√3}}}{{2}} : 2.

A special right triangle where the angles are both 45 degrees and 90 degrees. The sides are in the ratio 1 : 1 : @@ ext{√2}.

The hypotenuse is twice the length of the shorter leg (1). If the shorter leg is 'a', then hypotenuse = 2a.

The longer leg is equal to the shorter leg multiplied by $$\text{√3}$$ . If the shorter leg is 'a', then longer leg = $$a\text{√3}$$ .

Both legs are equal in length. If one leg is 'a', then the other leg is also 'a'.

The hypotenuse is equal to one leg multiplied by $$\text{√2}$$ . If one leg is 'a', then hypotenuse = $$a\text{√2}$$ .

The longest side is called the hypotenuse.

The longer leg is $$5\text{√3}$$ .

The hypotenuse is $$6\text{√2}$$ .

The shorter leg 'a' is 6.