Please agree to accept our cookies. If you continue to use the site, we'll assume you're happy to accept them.

# Trigonometry : Key Stage 5 (AS-Level) : Mathematics Content Knowledge

Key Stage

Topic
Questions

Next

Self-evaluation Tools
Currently viewing
Key Stage 5 (AS-Level)
Trigonometry
Question 1 of 11

# 1. How confident are you that you can use the cosine rule to:

## Example

Cosine rule: in any triangle ABC with lengths a, b, c:

c2 = a2 + b2 – 2ab cos C

The labelling of the triangle is arbitrary except that a is the length opposite vertex Ab is the length opposite vertex B and so on.

The cosine rule can also be written as:

a2 = b2 + c2 – 2bc cos A
or b2 = a2 + c2 – 2ac cos B

Example 1:
In triangle ABC, AC = 17cm, BC = 9cm and angle ACB = 20°. Calculate length AB.

Using the cosine rule gives

AB2 = 92 + 172 – 2 × 9 × 17 cos 20°
AB2 = 82.45
AB = 9.08 cm which is the length to 2dp.

Note that the cosine rule works for any triangle including right-angled triangles. When you have a right-angled triangle the cosine rule defaults to Pythagoras’ Theorem.

Example 2:
In triangle ABC:
a = 12 cm
b = 6 cm
c = 8 cm

From the cosine rule:
b2 = a2 + c2 – 2ac cos B

This gives 62 = 122 + 82 – 2 × 12 × 8 cos B

Therefore
36 = 144 + 64 – 182 cos B
36 = 208 – 192 cos B
–172 = –192 cos B
cos B =

 172 192
=
 43 48

## Related information and resources from other sites

 Add to your NCETM favourites Remove from your NCETM favourites Add a note on this item Recommend to a friend Comment on this item Send to printer Request a reminder of this item Cancel a reminder of this item