Triangle Identities

You might like to read our page on Trigonometry first!

Triangle Identities

Triangle identities are equations that are true for all triangles (they don't need to have a right angle).

For the identities involving right angles triangles see Trigonometric Identities.

Law of Sines


The Law of Sines (also known as The Sine Rule) is:

asin(A) = bsin(B) = csin(C)

it can also be this way around:

sin(A)a = sin(B)b = sin(C)c

Law of Cosines

The Law of Cosines (also known as The Cosine Rule) is an extension of the Pythagorean Theorem to any triangle:

c2 = a2 + b2 − 2ab cos(C)

which can be re-arranged to:

cos(C) = a2 + b2 − c22ab

Law of Tangents

The Law of Tangents is:

a + ba − b = tan[½(A+B)]tan[½(A−B)]


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