Q26 of 805 Page 1

A man in a boat rowing away from a light house 100 m high takes 2 minutes to change the angle of elevation of the top of the light house from 60⁰ to 30⁰. Find the speed of the boat in metres per minute. [Use ]


Or


Two poles of equal heights are standing opposite to each other on either side of the road, which is 80 m wide. From a point between them on the road, the angle of elevation of top of the poles are 60⁰ and 30⁰ respectively. Find the height of the poles and the distances of the point from the poles.


ACB = 60⁰ and ADB = 30⁰


Let, the length of CD = x m


And the length of CB = y m




y = 57.73 m




x + y = 173 m


x = 115.27 m


Speed of the boat = Distance/Time



= 57.635 m/min


Or



AEB = 60⁰ and DEC = 30⁰


Let, length of BE = x m


And length of two equal poles = h m


Then, length of EC = 80 – x m




…(1)




…(2)


From eq (1) and eq (2)


80 – x = 3x


x = 20 m


h= 20√3 m


So, the length of BE = 20 m


length of EC = 80 – 20 m = 60 m


length of two equal poles = 20√3 m


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