Trekantlikningen

Trekantlikningen refers to the set of equations that relate the sides and angles of a triangle. In this framework, a triangle can be described either by its three sides or by its three angles, and the relationships between these elements are captured by a small number of fundamental formulas. The concept underpins many geometric and trigonometric calculations.

Key relations include the triangle inequality, which states that for side lengths a, b, and c of a triangle, the sum of any two sides must exceed the third (a + b > c, a + c > b, b + c > a). The interior angles of a triangle always sum to 180 degrees. Quantitative tools commonly grouped under the trekantlikningen are the Pythagorean theorem for right triangles, the Law of Sines, and the Law of Cosines. The area can be computed as A = 1/2 ab sin C, where a and b are sides enclosing angle C, or by Heron’s formula when all three sides are known.

These relationships enable solving for unknown sides or angles given partial information. For example, the Law of Cosines states c^2 = a^2 + b^2 - 2ab cos(C), with c opposite angle C. The trekantlikningen framework thus provides a practical, widely used toolkit for problems in geometry, trigonometry, and applications such as surveying, architecture, computer graphics, and physics.