This is a method of finding some parameters inside a triangle in I/GCSE Mathematics.

The Cosine Rules

In I/GCSE Mathematics, the Cosine rule can be used to find:

- An unknown side when two sides of the triangle and the included angle are given.
- An unknown angle when 3 sides are given.

For finding an unknown sides **a**, the equation will be defined as

**a**^{2} = b^{2} + c^{2} – 2bcCosA

For finding an unknown angles the 3 formula for sides need to be re-arranged in terms of Cos A, B or C.

2bc**CosA** = b^{2} + c^{2} – a^{2}

**CosA** = b^{2} + c^{2} – a^{2 }/ 2bc

Therefore, applying the same method as earlier to the other sides produce similar formulae for b and c, namely:

**b**^{2} = a^{2} + c^{2} – 2acCosB

**c**^{2} = a^{2} + b^{2} – 2abCosC

Therefore, applying the same method as earlier to the other angles produce similar formulae for b and c, namely:

**CosB** = a^{2} + c^{2} – b^{2 }/ 2ac

**CosC** = a^{2} + b^{2} – c^{2 }/ 2ab

To find an unknown side we need 2 sides and the included angle.

**a**^{2} = 8^{2} + 9.6^{2} – 2 x 8 x 9.6 x Cos 40^{o}

**a** = SqRoot(8^{2} + 9.6^{2} – 2 x 8 x 9.6 x Cos 40^{o})

**a** = __6.2 cm__ (1 dp)

In I/GCSE Mathematics, to find an unknown angle we need 3 given sides.

**CosA** = (8^{2} + 9.6^{2} – 6.2^{2 )}/ (2 x 8 x 9.6)

**A** =40^{o}

You finish reading and completing in cosine rule in I/GCSE Mathematics.

Well done!