Special right triangle triangles are used to aid in calculating common trigonometric functions, as below: The 45°–45°–90° triangle, the 30°–60°–90° triangle, and the equilateral/equiangular (60°–60°–60°) triangle are the three Möbius triangles in the plane, meaning that they tessellate the plane via reflections in their sides; see Triangle group. In plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1 : 1 : 2, adding up to 180° or radians. Hence, the angles respectively measure 45° (), 45° (), and 90° (). The sides in this triangle are in the ratio 1 : 1
Triangle length of the other sides and the angle opposite to the unknown side. As per the law: For a triangle with length of sides "a", "b", "c" and angles of α, β, γ respectively, given two known lengths of a triangle "a" and "b", and the angle between the two known sides γ (or the angle opposite to the unknown side "c"), to calculate the third side "c", the following formula can be used: If the lengths of all three sides of any triangle are known the three angles can be calculated: The law of tangents, or tangent rule, can