 Hello and welcome to the session let us discuss the following question it says the angle of elevation of the top of the tower as observed from a point on the ground is alpha and on moving A meters towards the tower the angle of elevation is beta prove that the height of the tower is A tan alpha into tan beta upon n beta minus 10 alpha. So let's now move on to the solution. So this is the tower denote this by A, B, C. A, B be the tower h meter distance of a point on the ground from the tower be x meter. So this distance is x that is C, B is x meter. Now we are given that if we move A meter towards building then the angle of elevation becomes beta becomes beta this point be D. So now in right triangle A, B, C we have perpendicular upon base is equal to tan alpha that is A, B upon B, C is equal to tan alpha. Now A, B is the height of the tower so this implies h upon x is equal to tan alpha so this implies h is equal to tan alpha into x x tan alpha. Now if we move A meter towards the building the angle of elevation becomes BD. So in triangle A, B, D upon B, D equal to tan beta now again A, B is the height and BD is x minus A since this whole distance is x meter. So this much is x minus A is equal to tan beta so this implies h is equal to x minus A into tan beta. Let's say this has one and this has two. Now equating 1 and 2 is equal to x minus A tan beta because both gives us the height of the tower h is equal to x tan alpha and h is equal to x minus A tan beta. So they are equal this implies x tan alpha is equal to x tan beta minus A tan beta so this implies A tan beta is equal to x tan beta minus x tan alpha and this implies A tan beta is equal to x into tan beta minus tan alpha and this implies x is equal to A tan beta upon tan beta minus tan alpha. Now from 1 we have h is equal to x tan alpha now x is this so substituting we have h is equal to A tan beta upon tan beta minus tan alpha into tan alpha. Hence we have proved that h is equal to A into alpha tan beta upon tan beta minus tan alpha. So this completes the question and the session right for now take care have a good day.