Anonymous

# a ship leaves point p then sails 285km at 40 degrees north of west.?

in which direction must it now head and far must it sail so its resultant displacement will be 115km directly east of point p? thanks

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- Anonymous8 years agoBest Answer
The ship has gone 285 . sin 40 km North and 285 . cos 40 West

To get to 115 km East the ship must go

285 . sin 40 South and ( 285 cos40 + 115 ) East

The distance will be sq. rt. ( (285 sin40)^2 + ( 285.cos40 +115)^2 )

the angle is East ( tan^-1 ( 285 sin 40 / ( 285 cos 40 + 115 ) )

Source(s): Old teacher - J-ELv 58 years ago
Use law of sines and law of cosines

law of cosines to find the distance to travel

d² = 285² + 115² - 2x285x115xcosA with A = 180°-40° = 140°

d² = 144664.2132

d = 380.3474901 km

law of sines to find the angle

d/sin140 = 285/sinB

sinB = 285sin140 /d = .481650... ====> B = 28.8°

distance = 380.35km , 28.8° south of east

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