Apps. and Interpretation for IBDP Maths Ebook 1 | Page 177

(b) (i) ABC ˆ �180 � 44.61291137 � 64 (M1) for valid approach
ABC ˆ � 71.38708863
ABC ˆ � 71.4
A1 N2
(c)
(ii)
(i)
AC �16.8 �21.5
2 2 2
�2(16.8)(21.5) cos 71.38708863
AC � 22.66979298
AC � 22.7 cm
A1 N3
(M1)(A1) for substitution
2 2 2
ˆ 12 �12 �22.66979298
cos AOC �
2(12)(12)
(M1)(A1) for substitution
AOC ˆ � 141.6691693
AOC ˆ � 142
A1 N3
[5]
13
(ii)
reflex AOC ˆ �360 � 141.6691693 (M1) for valid approach
reflex AOC ˆ � 218.3308307
The length of arc ABC
218.3308307
�2 � (12) �
360
(A1) for substitution
� 45.72710224
� 45.7 cm
A1 N3
[6]
Exercise 47
1. Consider a circle with centre O and radius 14 cm. Triangle ABC is drawn such that its
vertices are on the circumference of the circle.
AB � 20.8 cm , AC � 26.6 cm and ABC ˆ � 71.5
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