4MA1/2H Jun 2019, Question 19: Area of a Triangle Using Sine
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2H (Higher) · Calculator · 6 marks
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The question, in short
Quadrilateral ABCD split by diagonal AC; AD = 26 cm, angle CAD = 39°, triangle ACD area 250 cm², angle ABC = 95°, angle ACB = 47°. Find the total area of ABCD to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 6 marks
- 1Triangle ACD: 250 = ½ × 26 × AC × sin 39°
- 2AC = 250 ÷ (13 × sin 39°) = 30.56…
- 3Angle BAC = 180° − 95° − 47° = 38°
- 4Sine rule: AB = 30.56… × sin 47° ÷ sin 95° = 22.43…
- 5Area ABC = ½ × 30.56… × 22.43… × sin 38° = 211.0…, total = 250 + 211.0… = 461
Answer461
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