Q22 of 35 Page 219

Two poles are x metres apart and the height of one is double than that of the other. If from the mid – point of the line joining their feet, an observer finds the angle of elevation of their tops to be complementary, then the height of the shorter pole is

Let the height of the poles be h and 2h respectively.


Let the angles of elevation of the top of the poles from the midpoint M of the line joining the feet of the poles be α and ß.


Also, given that they are complementary angles, α + ß = 90⁰



From the figure we see that,


and


and


Now,



tan (90 – α) = 2 tan α


cot α = 2 tan α





Now,





The height of the shorter pole is .

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