Question

fast
class 10
chapter 8or 9
no spam

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)