Analysis and Approaches for IBDP Maths Ebook 1 | Page 115

Front Page
39
Paper 1 Section A – Areas of triangles and sectors
Example
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 line.
AB � 3 3 cm , BD � 3 cm , area of triangle
ABC
27
cm
4
2
� , ˆ
ABC is acute.
(a) Find ˆ ABC .
(b)
Find the exact area of the sector BDC.
[5]
[3]
Solution
(a)
27 2
Area of triangle ABC � cm
4
1 ˆ 27
� (AB)(BC)sin ABC �
2 4
(M1) for area formula
BC � BD
1 ˆ 27
� (3 3)(3)sin ABC �
2 4
(A1) for substitution
9 3 ˆ 27
sin ABC �
2 4
(A1) for simplification
sin ABC ˆ �
3
2
(A1) for simplification
ABC ˆ �
� 3
A1 N3
[5]
11
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