# Right Triangle

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

#### 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.

### 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.

### 3

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

#### 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.

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.