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 \({\rm{B\hat OC}}\) is 60°. 

Calculate the size of the angle \({\rm{B\hat AC}}\).

AC = AB = 10 (cm)     A1

triangle OBC is equilateral     (M1)

BC = 6 (cm)     A1

EITHER

\({\rm{B\hat AC}} = 2\arcsin \frac{3}{{10}}\)     M1A1

\({\rm{B\hat AC}} = 34.9^\circ \,\,\,\,\,\)(accept 0.609 radians)     A1

OR

\(\cos {\rm{B\hat AC = }}\frac{{{{10}^2} + {{10}^2} - {6^2}}}{{2 \times 10 \times 10}} = \frac{{164}}{{200}}\)     M1A1

\({\rm{B\hat AC}} = 34.9^\circ \,\,\,\,\,\)(accept 0.609 radians)     A1

Note: Other valid methods may be seen.

[6 marks]

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