Question

the angle of elevation of the top of a top of a tower from a point on the same level as the foot of the tower is on advancing 'p' metres towards the foot of the tower the angle of elevation becomes B9 beta). Show that the height 'h' of the tower is given by - h{p tan alpha tan beta/tan beta -tan alpha}

Answer 1

see pic ,

tanß = H/x

H =xtanß --------(1)

tan∅ = H/(x +P)

Ptan∅ +xtan∅ = H
put equation (1)

Ptan∅ +Htan∅/tanß =H

Ptan∅.tanß + H.tan∅ = H.tanß

Ptan∅.tanß = H(tanß -tan∅)

H = Ptan∅.tanß/(tanß -tan∅)