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Area of a triangle (by the one side and the sines of the triangle's angles)

A triangle is a polygon with three edges and three vertices. In a scalene triangle, all sides are unequal and equivalently all angles are unequal. When the ... more

Morley's trisector theorem

Morley’s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral ... more

Right triangle altitude theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the ... more

Altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the base (the opposite side of the triangle). This line ... more

Morley's trisector theorem (area)

Morleyâ€™s trisector theorem states that in any triangle, the three points of intersection of the adjacent angle trisectors form an equilateral triangle, ... more

Area of an arbitrary triangle

The area of an arbitrary triangle can be calculated from the two sides of the triangle and the included angle.
... more

Relation between the sides of an Equilateral triangle and its circumradius and inradius

An equilateral triangle is a triangle in which all three sides are equal. In traditional or Euclidean geometry, equilateral triangles are also equiangular; ... more

Hyperbolic law of cosines - 1st law

In hyperbolic geometry, the law of cosines is a pair of theorems relating the sides and angles of triangles on a hyperbolic plane, analogous to the planar ... more

Area of an arbitrary triangle (incircle and excircles)

The incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides. The center of ... more

Spherical Law of Cosines (cosine rule for angles)

In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, ... more

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