EDEXCEL GCSE MATHS · HIGHER
Exam Practice: The cosine rule
The cosine rule and 2D trigonometric problems · More trigonometry · Lesson 6 of 9 · 17 marks · 30 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 WORK OUT (3 marks)
In triangle PQR, PQ = 8.4 cm, PR = 6.1 cm and angle QPR = 57°. Work out the length of QR. Give your answer correct to 3 significant figures.
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(Total for Question 1 = 3 marks)
Question 2 WORK OUT (3 marks)
In triangle ABC, AB = 8 cm, AC = 6 cm and angle BAC = 40°. Work out the length of BC. Give your answer correct to 3 significant figures.
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(Total for Question 2 = 3 marks)
Question 3 WORK OUT (3 marks)
A triangle has sides of length 6 cm, 8 cm and 11 cm. Work out the size of the largest angle. Give your answer correct to 1 decimal place.
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(Total for Question 3 = 3 marks)
Question 4 WORK OUT (3 marks)
A ship sails 12 km on a bearing of 040°. It then sails 9 km on a bearing of 130°. Work out the distance of the ship from its starting point.
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(Total for Question 4 = 3 marks)
Question 5 WORK OUT (3 marks)
A triangle has sides of length 7 cm, 8 cm and 9 cm. Work out the size of the smallest angle. Give your answer correct to 1 decimal place.
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(Total for Question 5 = 3 marks)
Question 6 EXPLAIN (2 marks)
In triangle ABC, you are given a, c and angle B. Which rule would you use to find b, the sine rule or the cosine rule? Give a reason.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 17 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
QR² = 8.4² + 6.1² − 2 × 8.4 × 6.1 × cos 57°= 51.95, so QR = 7.21 cm
• 8.4² + 6.1² − 2 × 8.4 × 6.1 × cos 57° M1
• 51.9... A1
• 7.21 A1
Question 2 (3 marks)
BC² = 6² + 8² − 2 × 6 × 8 × cos 40°= 26.46, so BC = 5.14 cm
• 6² + 8² − 2 × 6 × 8 × cos 40° M1
• 26.4... A1
• 5.14 A1
Question 3 (3 marks)
cos A = (6² + 8² − 11²)/(2 × 6 × 8) = −0.21875, so A = 102.6°
• (6² + 8² − 11²)/(2 × 6 × 8) M1
• −0.21875 A1
• 102.6 A1
Question 4 (3 marks)
The angle between the two legs is 130°− 40°= 90°, so the distance is √(12² + 9²) = √225 = 15 km.
• Right angle identified M1
• 12² + 9² = 225 M1
• 15 A1
Question 5 (3 marks)
cos A = (8² + 9² − 7²)/(2 × 8 × 9) = 0.6667, so A = 48.2°
• (8² + 9² − 7²)/(2 × 8 × 9) M1
• 0.666... A1
• 48.2 A1
Question 6 (2 marks)
The cosine rule, because two sides and the angle between them are known and there is no matching side and angle pair.
• Cosine rule B1
• Two sides and the included angle B1