Apps. and Interpretation for IBDP Maths Ebook 1 | Page 172

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Solution
(a)
EAC ˆ �180 � 128
EAC ˆ � 52
(A1) for correct value
The bearing of A from E
�360 � 52
� 308
A1 N2
(b) (i) ACE ˆ �180 �52 � 70
(M1) for valid approach
ACE ˆ � 58
A1 N2
(c)
(ii)
AE 300
�
sin58 sin 70
(M1)(A1) for substitution
AE � 270.7421802
AE � 271 km A1 N3
2 2 2
DE �(400) �270.7421802
�2(400)(270.7421802) cos 52
(M1)(A1) for substitution
DE � 316.153292
DE � 316 km
A1 N3
(d) (i) Note that B lies on AC such that
BE � AC . (M1) for valid approach
ˆ BE
sin EAC � AE
sin52
BE
�
270.7421802
BE � 213.3477495
BE � 213 cm A1 N2
(ii) Let v km/h be the speed of the ferry.
BE DE
�
v 100
(M1) for valid approach
213.3477495 316.153292
�
v
100
(A1) for substitution
v � 67.4823748
Thus, the speed of the ferry is 67.5 km/h. A1 N3
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