4MA1/1H Jan 2023, Question 16: Choosing Between Sine and Cosine Rules
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
Use triangle ABC with AC = 24 cm, BC = 31 cm and angle BAC = 64°, plus CD = 16 cm and CE = 19 cm, to calculate DE to 3 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1sin ABC ÷ 24 = sin 64° ÷ 31
- 2sin ABC = 24 × sin 64° ÷ 31 = 0.6958...
- 3Angle ABC = 44.09...°
- 4Angle ACB = 180° − 64° − 44.09...° = 71.90...°
- 5ACD and BCE are straight lines, so angle DCE = angle ACB = 71.90...°
- 6DE² = 16² + 19² − 2 × 16 × 19 × cos 71.90...°
- 7DE² = 617 − 608 × 0.3105... = 617 − 188.83... = 428.16...
- 8DE = √428.16... = 20.69...
- 9DE = 20.7 cm
Answer20.7
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