0580/13 Oct/Nov 2021, Question 24: Choosing the Right Trigonometric Ratio
Cambridge IGCSE Mathematics 0580 · Paper 13 (Core) · Calculator · 5 marks
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The question, in short
Use two right-angled triangle diagrams to find a hypotenuse from two given sides, and show a second hypotenuse rounds to 5.9 to 2 significant figures.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Part (a) · 2 marks
In the right-angled triangle with sides 12.9 cm and 8.6 cm, calculate the hypotenuse x.
- 1x² = 12.9² + 8.6² = 166.41 + 73.96 = 240.37
- 2x = √240.37 = 15.50…
Answer15.5 or 15.50...
Part (b) · 3 marks
In the right-angled triangle with vertical side 3.8 cm and top angle 50°, show the hypotenuse y is 5.9 to 2 significant figures.
- 1The 3.8 cm side is adjacent to the 50° angle and y is the hypotenuse
- 2cos 50° = 3.8/y
- 3y = 3.8 ÷ cos 50° = 3.8 ÷ 0.6427… = 5.91…
- 45.91… = 5.9 to 2 significant figures
Answer5.91...
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