Fishing Boat Diagram
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Bearings Problem?
Can you please help me with this maths problem? Please explain how you get the answer too.
A diagram can be found here: http://img503.imageshack.us/img503/5846/triio0.jpg
A very small island A is on the bearing of 036 from a port P on the mainland.
A fishing boat at B is on a bearing of 070 from A.
The boat is 9.7km from A and 21.3km from P.
Calculate the bearing of B from P.
Let x be the required bearing.
Then:
Equating distances east from P:
PA sin(36) = 21.3 sin(x) - 9.7 sin(70) .......(1)
Equating distances north from P:
PA cos(36) = 21.3 cos(x) - 9.7 cos(70) ....(2)
Equating PA from (1) and (2):
( 21.3sin(x) - 9.7sin(70) ) / sin(36)
= ( 21.3 cos(x) - 9.7 cos(70) ) / cos(36)
Multiply by cos(36)sin(36):
21.3sin(x)cos(36) - 9.7sin(70)cos(36)
= 21.3cos(x)sin(36) - 9.7sin(36)cos(70)
Hence:
21.3 sin(x - 36) = 9.7 sin(70 - 36)
sin(x - 36) = 9.7sin(34) / 21.3
x = 36 + arcsin( 9.7sin(34) / 21.3 )
= 50.75 deg.
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