Sine rule

The sine rule can be used to find an angle or side if we know:

• a side lenght
• the size of the angle opposite that side
• any other side or angle

The triangle

The lengths a, b and c represent the side lengths in this triangle.
The angles A, B and C represent the angles in the triangle.

            A
          /   \
     c  /       \  b
      /           \
    /               \
   B ---------------- C
            a

The sine rule formula

Using the triangle above, the sine rule tells us that:

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

and, equivalently:

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

This means that the ratio of a side length to the sine of its opposite angle is the same for all three sides and angles in the triangle.