maths F.3 URGENTTTTT..

2008-09-02 6:42 am
Two ships A and leave a port at the same time. Ship A sails on a bearing of 300 degree for 12 km while ship B sails on a bearing of 150 degree for 12 km. Find
(a) the distance between the two ships
(b) the ebaring of ship A from ship B
(c) teh bearing of ship B from ship A

回答 (1)

2008-09-02 12:02 pm
✔ 最佳答案
A bearing in this context is the same as an azimuth, i.e. the angle measured clock-wise from the north.

From the port, shipA sails on a bearing of 300 degrees, which is the same as N60W, for 12 km..
Ship B sails on a bearing of 150 degrees, or S30E, for 12 km.

A simple diagram reveal that the two ships A, B and the port make an isosceles triangle with equal sides PA and PB of length 12 km. The angles PAB and PBA are equal to 15 degrees.

(a) the distance between the two ships
The distance D, between the two ships A and B is thus

D=2*12cos(15)= 23.4755 km

(b) the ebaring of ship A from ship B
The bearing of ship A from ship B is the same as the bearing of the port from B minus 15 degrees
= 150 + 180 -15 = 315 degrees

(c) teh bearing of ship B from ship A
The bearing of ship B from ship A is the bearing of the port from A plus 15 degrees
= 300 - 180 + 15 = 135 degrees

Note that this answer is the inverse of the answer in B by checking
135+180 = 315.


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