Apps. and Interpretation for IBDP Maths Ebook 1 | Page 171

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Example
Paper 2 – Bearing and Speed Problems
13
A ship is sailing south from a point A towards point D . Point C is 300 km south of A .
Point D is 100 km south of C . There is a lighthouse at E . The bearing of E from A is
128 . The angle AEC is 70 . This is shown in the following diagram.
(a) Find the bearing of A from E .
(b) (i) Find the size of the angle ˆ ACE .
[2]
(ii) Hence, find the length of AE .
[5]
(c) Find the length of DE .
[3]
When the ship reaches D , it changes direction and travels directly to the lighthouse at
100 km per hour. At the same time as the ship changes direction, a ferry starts travelling
to the lighthouse from a point B . This point B lies on AC , between A and C , and is
the closest point to the lighthouse. The ship and the ferry arrive at the lighthouse at the
same time.
(d) (i) Find the length of BE .
(ii)
Hence, find the speed of the ferry.
[5]
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