Apps. and Interpretation for IBDP Maths Ebook 1 | Page 173

Exercise 46
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.
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(a) Find the bearing of C from E .
(b) (i) Find the size of the angle ˆ AEC .
[2]
(ii) Hence, find the length of AE .
[5]
(c) Find the length of 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.
(i) Find the length of BE .
(ii)
Hence, find the speed of the boat.
[5]
2. The following diagram shows the quadrilateral ABCD.
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