Special Right Triangles

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths. The two main types are the 45-45-90 triangle and the 30-60-90 triangle.

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is $$\text{leg} \times \text{√2}$$ .

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 : $$\text{√3}$$ : 2, where 1 is the length of the side opposite the 30-degree angle.

The hypotenuse is $$4\text{√2}$$ .

The longer leg is $$5\text{√3}$$ .

The hypotenuse is twice the length of the shorter leg.

Each leg is 8.

The shorter leg is 6, and the hypotenuse is 12.

It is a 30-60-90 triangle.

The sum of the angles in a right triangle is always 180 degrees, with one angle being 90 degrees.