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Date May 2010 Marks available 6 Reference code 10M.2.hl.TZ1.3
Level HL only Paper 2 Time zone TZ1
Command term Calculate Question number 3 Adapted from N/A

Question

In the right circular cone below, O is the centre of the base which has radius 6 cm. The points B and C are on the circumference of the base of the cone. The height AO of the cone is 8 cm and the angle BˆOC is 60°. 

 

Calculate the size of the angle BˆAC.

Markscheme

AC = AB = 10 (cm)     A1

triangle OBC is equilateral     (M1)

BC = 6 (cm)     A1

EITHER

BˆAC=2arcsin310     M1A1

BˆAC=34.9(accept 0.609 radians)     A1

OR

cosBˆAC=102+102622×10×10=164200     M1A1

BˆAC=34.9(accept 0.609 radians)     A1

Note: Other valid methods may be seen.

 

[6 marks]

Examiners report

The question was generally well answered, but some students attempted to find the length of arc BC.

Syllabus sections

Topic 3 - Core: Circular functions and trigonometry » 3.7 » The cosine rule.

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