Question

A window of a house is h metre above the ground. From the window, the angles of ekvation and depression of the top and bottom of another house situated on the ite side of the lane are found to be and respectively. Prove that the height incert exemplari dthe house is h (1 + tan a tan) metres.

Answer 1

I think answer should be
height of another house is h(1 + tanα.cotβ)


see the attachment,
Let AE is the window of one house which is h m metre above from the ground . from the window , angle of elevation (α ) and angle of depression ( β ) of the top and bottom of another house of height BD is shown in figure.

now, AE = BC = h ---------(1)

from ∆BCE ,
tanβ = BC/CE = h/CE
CE = h/tanβ -------(2)

from ∆DEC ,
tanα = DC/CE
from equation (1) CE = h/tanβ = hcotβ, put it here,

tanα = DC/hcotβ
DC = h.tanα.cotβ --------(3)

now, we can see that height of another house is BD
BD = BC + CD
from equations (1) and (3)
BD = h + h.tanα.cotβ = h(1 + tanα.cotβ)