Plane Trigonometry

General Triangle

Area of Triangle

The area of any triangle is one-half the product of any of its two sides and their included angle (angle between the sides).


A = ½ ab sin C = ½ ac sin B = ½ bc sin A


Area of Triangle in Terms of the Sides (Heron's Formula, Hero of Alexandria)

Sum of Interior Angles


A + B + C = 180°


Sine Law:

In any triangle, the ratio of any side to the sine of its opposite angle is constant. This constant ratio is the diameter of the circumscribing circle.

Cosine Law:

The square of a side of a plane triangle equals the sum of the squares of the remaining sides minus twice the product of those sides and the cosine of the angle between them.

Law of Tangents

A statement about the relationship between the tangents of two angles of a triangle and the lengths of the opposing sides.

Mollweide's Formula

Sometimes referred to in older texts as Mollweide's equations, named after Karl Mollweide, is a set of two relationships between sides and angles in a triangle.