The sine rule
The sine rule allows you to calculate sides and angles of a triangle, if you know:
  • the length of two sides and the size of the angle opposite one of them, or...
  • two angles and the length of a side opposite one of them.
Start with a general triangle, with the angles labelled P, Q & R and the sides opposite them labelled p, q & r like this:

For this triangle, the sine rule states that:

By selecting any two parts of the rule, and rearranging the equation, you can find any component. For example, if you knew side p, angle P and angle R, you could find side p like this:

Most recently updated at 18:31 (British time) on 07 April 2004