# Non-right angled triangles

### The cosine rule

$a^2=b^2+c^2-2bc\cos(A)$
$b^2=a^2+c^2-2ac\cos(B)$
$c^2=a^2+b^2-2ab\cos(C)$

### The sine rule

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

### The area of a non-right angled triangle

$\frac{1}{2}ab\sin(C)$

Note that to maintain accuracy, store values on your calculator and leave rounding until the end of the question. You can round when jotting down working but you should retain accuracy throughout calculations.

## Example 1

Find the length of the side marked x in the following triangle:

## Example 2

Find the angle marked x in the following triangle: