A vertical tower stands on a horizontal plane and is surrounded by a vertical flagstaff of height 'n' .At a point on the plane the angle of elevation of the bottom of the flagstaf is ,'alpha' and that of the top of flagstaff is 'beta' . prove that height of the tower is h tan alpha/tan beta-tan alpha

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2014-11-26T08:17:43+05:30

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We have a tower AB of height H .  On top of it, we have a flagstaff BC of height h.  From a point P on the plane
         the angle of elevation of B is APB = α
         the angle of elevation of C is APC = β
    
              tan α = H / AP         tan β = (H + h)  / AP

         =>   h = AP ( tan β - tan α)  = (H / tan α) * (tan β - tan α)

               H = height of tower =  h tan α / ( tan β - tan α )


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