4MA1/1H Jan 2022, Question 21: Trigonometry in 3D: Cuboids
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 5 marks
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The question, in short
For the described prism with square face ABDE, equilateral triangle BCD, EF = 2 × AE and M the midpoint of GF, use tan y° = T for angle MAJ and find T in the form (√p + √q)/17.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 5 marks
- 1Let AE = 10, so EF = 20; M is 20 along and 5 across from A
- 2AM = √(20² + 5²) = √425 = 5√17
- 3Height of triangle BCD = √(10² − 5²) = 5√3, so JM = 10 + 5√3
- 4tan y° = JM ÷ AM = (10 + 5√3)/(5√17) = (2 + √3)/√17
- 5Rationalise: (2√17 + √51)/17, and 2√17 = √68, so T = (√68 + √51)/17
AnswerT = (√68 + √51)/17
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