A vertical tower Stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of Elevation of the bottom and the top of the flag staff are `alpha and beta` respectively Prove that the height of the tower is `(htanalpha)/(tanbeta - tanalpha)`

A vertical tower Stands on a horizontal plane and is surmounted by a v

1.	A vertical tower Stands on a horizontal plane and is surmounted by a vertical flag staff of height h. At a point on the plane, the angles of Elevation of the bottom and the top of the flag staff are `alpha and beta` respectively Prove that the height of the tower is `(htanalpha)/(tanbeta - tanalpha)`
Answer» We can draw a diagram with the given details. Please refer to video for the diagram. Here, height of the tower ` = BC = x` `AB = h, CD = y` `/_CDB = alpha, /_CDA = beta` `:.tan alpha = (BC)/(CD) ` `=> tan alpha = x/y` `y = x/ tan alpha->(1)` Now, `tan beta = (AC)/(CD) ` `=> tan beta = (h+x)/(y)` `=> y tan beta = h+x` Putting value of `y` from (1), `=>x/tan alpha tan beta= h+x` `=>x(tanbeta/tanalpha-1) = h` `=>x((tanbeta-tanalpha)/tanalpha) = h` `=>x = (htanalpha)/(tanbeta-tanalpha)` So, height of tower is `(htanalpha)/(tanbeta-tanalpha)`.