4MA1/1HR Jan 2019, Question 21: The Cosine Rule
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Use a triangle with sides 5, x, y, angle 60° and x = y − 1 to find the perimeter k.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1The 60° angle lies between the sides of length y and 5, and x is opposite it
- 2Cosine rule: x² = y² + 5² − 2 × y × 5 × cos60°
- 3cos60° = 0.5, so x² = y² + 25 − 5y
- 4x = y − 1, so (y − 1)² = y² + 25 − 5y
- 5y² − 2y + 1 = y² + 25 − 5y
- 6−2y + 1 = 25 − 5y
- 73y = 24
- 8y = 8
- 9x = 8 − 1 = 7
- 10Perimeter k = x + y + 5 = 7 + 8 + 5
- 11k = 20
Answer20
Stuck on a step? Read the free lesson: The Cosine Rule
Practise more the cosine rule questions
Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on the cosine rule
Also searched as: 4MA1 1HR January 2019 · 4MA1/1HR · 4ma1 jan19 1hr · question 21.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.