Question

Question #4395c

Answer 1

`(hcos(alpha-beta)sinalpha)/sinbeta`

Explanation:

Given

• `H->"Height of Tower"=CD`

• `h->"Height of Pole"=AB`

• `/_CBD->"Angle of elevation top of Tower from B "=alpha`

• `/_ACB->"Angle subtended by the pole at C "=beta`

• `/_CAE =(alpha-beta)`

• `"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`