EDEXCEL GCSE MATHS · HIGHER
Exam Practice: Areas and the sine rule
Calculating areas and the sine rule · More trigonometry · Lesson 5 of 9 · 18 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 ABC, AB = 7 cm, angle ABC = 40° and angle ACB = 75°. Work out the length of AC. 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, angle A = 52°, angle B = 71° and BC = 9.4 cm. Work out the length of AC. Give your answer correct to 3 significant figures.
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(Total for Question 2 = 3 marks)
Question 3 WORK OUT (3 marks)
In triangle ABC, BC = 7 cm, AC = 9 cm and angle BAC = 35°. Work out the size of angle ABC. Give your answer correct to 1 decimal place. (Angle ABC is acute.)
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(Total for Question 3 = 3 marks)
Question 4 WORK OUT (2 marks)
A triangle has two sides of length 9.5 cm and 6.2 cm with an angle of 112° between them. Work out the area of the triangle. Give your answer correct to 3 significant figures.
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(Total for Question 4 = 2 marks)
Question 5 WORK OUT (4 marks)
The area of a triangle is 25 cm². Two of its sides are 5 cm and 10 cm and the angle between them is acute. Work out the size of the angle between these two sides. Give your answer correct to 1 decimal place.
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(Total for Question 5 = 4 marks)
Question 6 EXPLAIN (3 marks)
In a triangle, angle A = 30°, a = 6 cm and b = 10 cm. Show that sin B = 5/6.
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(Total for Question 6 = 3 marks)
TOTAL FOR PAPER = 18 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (3 marks)
AC = (7 sin 40°)/(sin 75°) = 4.66 cm
• AC/(sin 40°) = 7/(sin 75°) M1
• (7 × sin 40°)/(sin 75°) M1
• 4.66 A1
Question 2 (3 marks)
AC = (9.4 sin 71°)/(sin 52°) = 11.3 cm
• AC/(sin 71°) = 9.4/(sin 52°) M1
• (9.4 × sin 71°)/(sin 52°) M1
• 11.3 A1
Question 3 (3 marks)
sin B = (9 sin 35°)/7 = 0.7375, so B = 47.5°
• (sin B)/9 = (sin 35°)/7 M1
• sin B = 0.7375... M1
• 47.5 A1
Question 4 (2 marks)
½ × 9.5 × 6.2 × sin 112°= 27.3 cm²
• ½ × 9.5 × 6.2 × sin 112° M1
• 27.3 A1
Question 5 (4 marks)
½ × 5 × 10 × sin C = 25, so sin C = 1, giving C = 90°.
• ½ × 5 × 10 × sin C = 25 M1
• 25 sin C = 25 M1
• sin C = 1 A1
• 90.0 A1
Question 6 (3 marks)
(sin B)/10 = (sin 30°)/6, so sin B = (10 × 0.5)/6 = 5/6.
• Sine rule set up M1
• sin 30°= 0.5 M1
• Completes the proof A1