# 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:

\frac{a}{sin(A)} = \frac{b}{sin(B)} = \frac{c}{sin(C)}

it can also be this way around:

\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{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:

c

^{2}= a^{2}+ b^{2}− 2ab cos(C)which can be re-arranged to:

cos(C) = \frac{a^{2} + b^{2} − c^{2}}{2ab}

## Law of Tangents

The Law of Tangents is:

\frac{a + b}{a − b} = \frac{tan[½(A+B)]}{tan[½(A−B)]}

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