Apps. and Interpretation for IBDP Maths Ebook 1 | Page 161

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Example
Paper 1 – Areas of Triangles and Sectors
13
The following diagram shows a triangle ABC and a sector BDC of a circle with centre
B and radius 3 cm. The points A , B and D are on the same straight line.
AB � 3 3 cm , BD � 3 cm , area of triangle
ABC
27
cm
4
2
� , ˆ
ABC is acute.
(a) Find the size of the angle ˆ ABC .
(b) Hence, write down the size of the angle ˆ CBD .
(c)
Find the exact area of the sector CBD.
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Solution
(a)
27 2
Area of triangle ABC � cm
4
1 ˆ 27
� (AB)(BC)sin ABC � (M1) for area formula
2 4
BC �BD � 3 cm
1 ˆ 27
� (3 3)(3)sin ABC � (A1) for substitution
2 4
ˆ 3
sin ABC �
2
ABC ˆ � 60
A1 N3
(b) 120 A1 N1
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