A2400 ch9a | Version 1.1 | September 2020
The cosine rule to find missing sides
A LEVEL LINKS
Scheme of work: 4a. Trigonometric ratios and graphs
Key points
• a is the side opposite angle A.
b is the side opposite angle B.
c is the side opposite angle C.
• You can use the cosine rule to find the length of a side when two sides and the included
angle are given.
• To calculate an unknown side use the formula .
• Alternatively, you can use the cosine rule to find an unknown angle if the lengths of all three
sides are given.
• To calculate an unknown angle use the formula .
Example 1 Work out the length of side w.
Give your answer correct to 3 significant figures.
w2 = 33.804 040 51...
w =
w = 5.81 cm
1 Always start by labelling the angles
and sides.
2 Write the cosine rule to find the
side.
3 Substitute the values a, b and A into
the formula.
4 Use a calculator to find w2 and
then w.
5 Round your final answer to 3
significant figures and write the
units in your answer.
222
2cosabc bc A=+-
222
cos
2
bca
A
bc
+-
=
222
2cosabc bc A=+-
222
87287cos45w=+-´´´ °
33.804 04051
