Question

the angle of elevation of the top of a tower from a point on the same level as the foot of the tower is alpha . on advancing "p" metres towards the foot of the tower , the angle of elevation becomes beta . show that the height "h" of the tower is given by h(p tan alpha *tan beta /tan beta - tan alpha)

Answer 1

consider the diagram mentally.so let AB be the height of the tower such that it is equal to h meters.now at at the point of angle of beta consider that point as D and the point at the angle alpha be C.so forming two equations,BD=h/tan beta.........(1)
and BD=h/tan alpha -p.so now the two heights are equal. on comparing both the equations, we get,h=p.(tan alpha.tan beta)/tan beta-tan alpha