from a window 60m high above the ground of a house in a street the angles of elevation and depression of the top and foot of another house on the opposite side of the streer are 60degree and 45degree respectively. show that the height of th opposite house is 60(1+ root3)

let AB be the height of the window and CD represent the height of the opp. house.Here, A represents the window and C & D are the top and foot of the opp. house. From A,draw a perpandicular AE to CD

So, CD=CE+ED

Also,AB=ED=60m

In triangle AEC, we have:-

tan60=CE/AE

or, root3=CE/AE

or, CE=AE x root3--------(1)

In tr. AED,we have:-

tan45=ED/AE

or, 1=60/AE

or,AE=60m-------(2)

Placing the value of AE from (2) to (1), we have :-

CE=60 x rt.3

Now, height of house=CD

But,CD=CE+ED

or, CD=60*rt.3+60

or, CD=60(rt.3 + 1)

Hence, we have showed that height of house is equal to