The Sine Rule

If we have a triangle, and we need to calculate angles and/or sides, we can only use simple trigonometry and Pythagoras theorem if the triangle is right angled. If the triangle is not right angled, then we must use general formulae which apply to any triangle. One of these is the Sine Rule. With the sides and angles of a triangle labelled as below, small letters labelling sides opposite large letters labelling angles, we may use the formula

We can use the Sine Rule in two ways:

To find an angle given two sides and an angle, or to find a side given a side and two angles. Even though the Sine Rule has three terms, we only ever use two of them at a time.

In the triangle above we need to find the angle C: We don't haveorso don't include theterm . We use the equation

In the diagram below we need to find the side a. We don't haveorso don't include theterm.

We use the equation

to 2 dp.

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