Right triangles

A right triangle is a triangle in which one of the angles is exactly $90^ ext{o}$. The side opposite the right angle is called the hypotenuse, and the other two sides are called legs. The sum of the other two angles is $90^ ext{o}$, so they are both acute.

Important properties

• One angle is $90^ ext{o}$ (right angle).

• The hypotenuse is the longest side.

• The other two angles are complementary (add up to $90^ ext{o}$).

• Right triangles allow the use of the Pythagorean theorem: $a^2 + b^2 = c^2$ where $c$ is the hypotenuse.

• Special right triangles (like $30^ ext{o}$-$60^ ext{o}$-$90^ ext{o}$ and $45^ ext{o}$-$45^ ext{o}$-$90^ ext{o}$) have predictable side ratios.