The Cosine 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 Cosine 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 may use the formula in two ways:

By labelling the sides and angles as required we can find the formula above to find a side when we have two sides and the angle between the two sides, or we have three sides and we want to find an angle.

By rearranging the formula to makethe subject –and labelling the sides as required we can find the angle


to 2dp.



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