SOLUTION: A ship travelling with a constant speed and direction is sighted from a light house. At this time it is 2.7km away on a bearing of 42. Half an hour later it is on bearing of 115 at

Question 1205529: A ship travelling with a constant speed and direction is sighted from a light house. At this time it is 2.7km away on a bearing of 42. Half an hour later it is on bearing of 115 at a distance of 76km from lighthouse. Find its speed in kilometer per hour
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
A ship travelling with a constant speed and direction is sighted from a light house. At this time it is 2.7km away on a bearing of 42. Half an hour later it is on bearing of 115 at a distance of 76km from lighthouse. Find its speed in kilometer per hour
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2 sides of the triangle are given.
Find the angle between them.
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Find the angles wrt to the positive x-axis.
Bearing of 042 degs ---> 48 degs
Bearing of 115 degs ---> -25 degs
The angle between the sides is 73 degs
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Use the Cosine Law: c^2 = a^2 + b^2 - 2ab*cos(73)
c^2 = 2.7^2 + 76^2 - 2*2.7*76*cos(73)
c^2 = 5663.3
c = 75.25 km
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It moved 75.25 kms in 1/2 hour
Speed = 150.5 km/hr
A fast boat.
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