Question

. A window of a house is 2 m above the ground . From the window ,the angles of elevation

and depression of the top and bottom of another house situated on the opposite side of the lane

are found to be 60 o and 45o

respectively. Find the height of the house.​

Answer 1

Answer:

Here is your answer

Step-by-step explanation:

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)

hence, \bold{BD=h(1+tan{\alpha}.cot{\beta})}hence,BD=h(1+tanα.cotβ)

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