# Side length

The **side length** is a special case of the length of a line in geometry . The side lengths of a polygon (polygon) are the distances between the respective two corners . The sum of all side lengths is the circumference .

## Side length of triangles

### Triangle sides in geometry and nature

The length of the sides of the triangle (in the case of flat triangles) is specified in a measure of length (mainly in meters, cm and km). But if you go from the usual geometry *to nature* or to trigonometric tasks of geodesy , a distinction must be made between horizontal and inclined sides:

- Either an elevation or zenith angle is specified for the distance,
- or it is reduced to the horizon (approximated by multiplying it by the cosine of the elevation angle ).
- However, because of the spherical earth , the height level must also be taken into account, or whether it was reduced to the geoid or an earth ellipsoid .

### Euclidean geometry

- A well-known Euclidean theorem states that the longest side of a triangle is always shorter than the sum of the other two sides ( triangle inequality ).
- The larger of two sides of a triangle is always opposite the larger angle. Conversely, the larger of two angles of a triangle is always opposite the longer side.

### Plane triangles and their special cases

- Triangles in which at least two side lengths are the same are called isosceles .
- Triangles in which all three sides are the same length are called equilateral .
- In a right triangle , the longest side is opposite the right angle and is called a hypotenuse . The two shorter sides are called cathets .

The proportions of the side lengths of a right triangle correspond to the angle functions of trigonometry .

### Spherical triangles

In spherical geometry (spherical geometry), the side length initially corresponds to the length of the corresponding great circle arc . Most of the time, however, the size of the corresponding center angle (in degrees ) is taken as the side length. This definition has the advantage that the radius of the sphere does not matter.

## Side length of polygons

The length of the sides of general polygons can be traced back to the calculations on the triangle via the diagonals .