Given
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#H->"Height of Tower"=CD#
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#h->"Height of Pole"=AB#
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#/_CBD->"Angle of elevation top of Tower from B "=alpha#
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#/_ACB->"Angle subtended by the pole at C "=beta#
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#/_CAE =(alpha-beta)#
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#"Let "AE=BD=b#
#"Now for "DeltaCBD ,(CD)/(BD)=H/b=tanalpha......(1)#
#"And for "DeltaCAE ,(CE)/(AE)=(H-h)/b=tan(alpha-beta)......(2)#
Dividing (2) by (1) we get
#(H-h)/H=tan(alpha-beta)/tanalpha#
#=>1-h/H=(sin(alpha-beta)cosalpha)/(cos(alpha-beta)sinalpha)#
#=>h/H=1-(sin(alpha-beta)cosalpha)/(cos(alpha-beta)sinalpha)#
#=>h/H=(cos(alpha-beta)sinalpha-sin(alpha-beta)cosalpha)/(cos(alpha-beta)sinalpha)#
#=>h/H=sin(alpha-alpha+beta)/(cos(alpha-beta)sinalpha)#
#=>h/H=sinbeta/(cos(alpha-beta)sinalpha)#
#=>H/h=(cos(alpha-beta)sinalpha)/sinbeta#
#=>H=(hcos(alpha-beta)sinalpha)/sinbeta#
