Apps. and Interpretation for IBDP Maths Ebook 1 | Page 155

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Example
Paper 1 – Solving Triangles
13
The following diagram shows triangle ABC .
AB � 10 cm , BC � 9 cm , and ABC ˆ � 97 .
(a) Find the length of AC .
(b) Find the size of the angle ˆ BAC .
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Solution
(a)
(b)
2 2 2
AC � AB � BC � 2(AB)(BC) cos ABC ˆ
(M1) for cosine rule
2 2 2
AC �10 �9 � 2(10)(9) cos97
(A1) for substitution
AC � 14.24557762
AC � 14.2 cm
A1 N3
sin BAC ˆ sin ABC ˆ
�
BC AC
(M1) for sine rule
sin BAC ˆ
sin 97
�
9 14.24557762
(A1) for substitution
ˆ
9sin 97
sin BAC � 14.24557762
BAC ˆ � 38.83397714
BAC ˆ � 38.8
A1 N3
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