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Geometry & MeasuresStudy Notes

Worked Example: Finding a Side

Part of Cosine Rule — GCSE Mathematics

This study notes covers Worked Example: Finding a Side within Cosine Rule for GCSE Mathematics. Revise Cosine Rule in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 4 of 4 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 4

Practice

12 questions

Recall

3 flashcards

Worked Example: Finding a Side

Find side a when b = 7cm, c = 9cm, and A = 60°.

Solution

a² = b² + c² - 2bc cos A

a² = 49 + 81 - 2(7)(9)cos 60°

a² = 130 - 126(0.5) = 130 - 63 = 67

a = √67 = 8.2 cm (1 d.p.)

Keep building this topic

Read this section alongside the surrounding pages in Cosine Rule. That gives you the full topic sequence instead of a single isolated revision point.

MethodWhen Sine Rule FailsThe Cosine Rule

Practice Questions for Cosine Rule

Which formula is the cosine rule for finding side a?

  • A. a² = b² + c² − 2bc cosA
  • B. a/sinA = b/sinB
  • C. a² = b² + c²
  • D. cosA = (b + c − a) / 2bc
1 markfoundation

Show that when angle A = 90°, the cosine rule reduces to Pythagoras' theorem.

2 marksstandard

Quick Recall Flashcards

Cosine Rule
a² = b² + c² - 2bc cos A
Cosine Rule
a² = b² + c² - 2bc cosA. Use for SAS or SSS. Like Pythagoras with a twist!

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