A man in a boat rowing away from a lighthouse 100m high takes 2 minutes to change angle of elevation of the top of a lighthouse from 60 degree to 45 degree find the speed of boat in metres per minute.
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Answer:
AB is a lighthouse of height 100m . Let the speed of boat be x meter per minutes and CD is the distance which man travelled to change the angle of elevation .
Therefore,
CD=2X [Distance= speed X time]
tan(60°) = AB/BC
√3= 100/BC
=> BC= 100/√3
tan(45°) = AB/BD
=> 1 = 100/BD
BD= 100*1
CD= BD-BC
2x = 300-100/1
=> x= 200/1
=> x = 200
using ,
√3=1.73
x=200/1.73
=> 115.60
hence the speed of boat is 115.60meteres per minute
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