Right Triangle

A right triangle has a right angle (90º) and two acute angles.

Right Triangle


Legs or Catheti

The catheti (singular: cathetus) are the sides opposite the acute angles and are the shorter sides of the right triangle.

Hypotenuse

The hypotenuse is the side opposite the right angle, and is the largest side of the right triangle.


Area of a Right Triangle

The area of a right triangle is equivalent to half the product of its legs.

Right TriangleArea of a Right Triangle Formula


Theorems

1 Pythagorean theorem


2

In all right triangles, the length one of the legs is a mean proportional between the hypotenuse and the projection on it.

Elements of a Right Triangle

Mean Proportional of a Right Triangle

Mean Proportional of a Right Triangle


3

In all right triangles, the height of the hypotenuse is a mean proportional between the two segments that it divides.

Elements of a Right Triangle

Mean Proportional of a Right Triangle


Examples

The hypotenuse of a right triangle measures 30 cm and the projection of a leg is 10.8 cm on the hypotenuse. Find the length of the other leg.

Right Triangle

Right Triangle Operations

Right Triangle Operations

In a right triangle, the projections of the legs on the hypotenuse are 4 and 9 cm in length. Calculate the height of the triangle.

Right Triangle

Right Triangle Operations

Right Triangle Operations