Question

From a window 60 m high above the ground of a house in street the angles of elevation and depression of the top and the foot of an another house on opposite side of street are 60 degree and 45 degree show that the height of the opposite house is 60×1+root 3 meter.

Answer 1

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

60(1+ root3)