Analysis and Approaches for IBDP Maths Ebook 1 | Page 130

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 43
1. A ship is sailing north from a point A towards point D . Point C is 800 km north of A .
Point D is 550 km north of C . There is an island at E . The bearing of E from A is
051 . The angle DCE is 77 . This is shown in the following diagram.
(a) Find the bearing of C from E .
[2]
(b) Find AE .
[5]
(c) Find DE .
[3]
(d) When the ship reaches D , it changes direction and travels directly to the island at
62 km per hour. At the same time as the ship changes direction, a boat starts
travelling east, to the island from a point B . This point B is at the north of D .
The ship and the boat arrive at the island at the same time. Find the speed of the
boat.
[5]
2. The following diagram shows the quadrilateral ABCD.
AD � 15 km , ACD ˆ � 58 , ACB ˆ � 56 , and the bearing of A from D is 160 .
(a)
Find AC.
(b) Find the area of triangle DAC .
[3]
[3]
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