The sine rule is a formula which allows us to calculate missing angles and missing lengths in triangles when we know certain other angles and lengths. This is not restricted to right-angled triangles. If a question has a right-angled triangle we can use the simpler trigonometric identity.

The sine rule formula is as follows and should be memorised:

Examples

1. Find the length of side c

2. Find angle ABC.

The teacher will show you how to derive this formula. You don’t need to be able to do this yourself, but it is good for you to see that the formula is logically arrived at and not just conjured out of thin air! Below, for reference, is a summary of how to derive this formula

Exercise

Let’s complete exercise 9 on pages 226 and 227 of the extended textbook:

The answers are below:

Further Questions

Answers