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

Right triangle with the right angle at point C.

• 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 .