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)]
745, 746, 1558, 7879, 7880, 1559, 3971, 3972, 7881, 7882