# Right triangle

A right-angled triangle is a triangle with a right angle.

## Terms

### Hypotenuse

As the hypotenuse is defined as the longest side of a right triangle. It is located opposite the right angle.

The ratio between the lengths of the other sides and the hypotenuse describes the Pythagorean theorem, which is also called Hypotenusensatz.

The midpoint of the hypotenuse is the center of the Thales circle the perimeter of the right triangle.

### Cathetus

As cathetus ( from the Greek káthetos, lowering Serene, plumb ) each of the two shorter sides is called a right triangle. The short sides are thus the two sides of the right triangle forming the right angle.

With respect to one of the two acute angles ( in the drawing) of the triangle, a distinction is the adjacent side of this angle ( the angle fitting cathetus ) and the opposite side ( the angle opposite cathetus ).

The foot of the altitude on the hypotenuse divides it into two hypotenuse. The Kathetensatz and the height set to make statements about the lengths of these sections.

## Sets

The relationship between the lengths of the other sides and the hypotenuse describes the Pythagorean theorem, which is also called Hypotenusensatz. ( The sentence is: If a and b are the side lengths of the other sides and c is the side length of the hypotenuse, then the equation a ² b ² = c ²)

In other words, the Pythagorean theorem states that the sum of the areas of the two squares on the other sides is equal to the area of the square on the hypotenuse. From this fact, follow the other sides and the level set ( see also set group of Pythagoras ).

The theorem of Thales states that every triangle in a semicircle is a right triangle. The midpoint of the hypotenuse is the center of the Thales circle the perimeter of the right triangle.

The foot of the altitude divides the hypotenuse into two hypotenuse. The Kathetensatz and the height set to make statements about the lengths of these sections.

The trigonometric functions describe the mathematical relationships between the angles and the aspect ratios.

## Calculation and design

A right-angled triangle is completely determined by three determination units: the right angle, one side and another side, or another angle.

- If both catheti given, can the triangle to the SWS case treat.
- Are a cathetus and the hypotenuse is given, the SSW- case is applied.
- If a non - right angle is given, can be determined with the angle sum of the third angle. Then you can treat the triangle to the WSW- case.

The heights of the short sides are the same with the other cathetus. Therefore, the orthocenter is the point. The circumcenter is the center of the hypotenuse. The focus is on the triangle on the straight line between orthocenter and circumcenter. See also Excellent points in the triangle.