Plane Trigonometry
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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.