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In a triangle with angles A, B,C and sides a, b, c with side a opposite angle A, side b opposite angle B, and side c opposite angle C:

If you know 2 of the angles (b and c), the third (a) can be calculated as the sum of the angles must be 180°: a = 180° - (b + c)

If you know 2 of the sides (b and c) and the angle between them (A), the third side (a) opposite the angle A can be calculated using the cosine rule:

a^2 = b^2 + c^2 - 2 b c cos A

If you know one side (a) and the angle opposite it (A), then if a side (b) is known, the angle opposite it (B) can be calculated, or if an angle (C) is known the side (c) opposite it can be calculated, using the sine rule:

(sin A)/a = (sin B)/b = (sin C)/c = 1/(2R)

where R is the radius of the circumcircle of the triangle.

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