3.17: Segment with given area and sine of the angle

0606/13/M/J/25 — Question 7 · 6 marks

3.17 diagram
In this question, all lengths are in centimetres and all angles are in radians.
The diagram shows a sector of a circle with centre OO and radius 66.
(a)
It is given that the area of triangle AOBAOB is 9 cm29\text{ cm}^{2}.
Find the value of sin⁡θ\sin\theta.
[2]
(b)
It is also given that the exact area of the shaded segment is (15π−9) cm2(15\pi - 9)\text{ cm}^{2}.
Find the exact length of the arc ABAB.
[4]