# Standard Symbols

Following symbols in relation to Î”ABC are universally adopted.

mâˆ BAC = A, mâˆ ABC = B, mâˆ BCA = C

A + B + C = Ï€

AB = c, BC = a, CA = b
• Semi-perimeter of the triangle = s =  So a + b + c = 2s.

• The radius of the circumcircle of the triangle, that is, circumradius = R.
• The radius of the incircle of the triangle, that is, inradius = r.
• Area of the triangle = S = Î”.

# Sine rule

The sine rule is .

Nepierâ€™s formula
1. tan
2. tan
3. tan

# Cosine rule

In a Î”ABC, we have cos A = ,
cos B = , cos C = .

Notes:
• The above proof will not change even if âˆ A is a right angle or an obtuse angle.
• If the lengths of the three sides of a triangle are known, we can find all the angles by using cosine rule because this rule gives us cos A, cos B, and cos C. We know that ABC are in (0, Ï€) and the cosine function is one-one in [0, Ï€]. So ABC are precisely determined. Similarly, if two sides (say b and c) and the included angle A are given, the cosine rule cos A =  will give us aand then knowing abc we can find B and C by the cosine rule.

Projection formula

a = c cos B + b cos C

b = a cos C + c cos A

c = a cos B + b cos A

Half angle formulas
1. i. sin

ii. sin

iii. sin
2. i. cos

ii. cos

iii. cos