Question

A window of a house is h metres above the ground. From the top of 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 α and β respectively. Prove that the height of the other house is given by
h (1+tan α cot β) metres. Plz tell i will mark him/her brainliest

Answer 1

Answer:

Let the height of other house be

′

H

′

.

Now, In △DEC,

⇒tanα=

EC

DC

=

EC

H−h

⇒EC=

tanα

H−h

⟶(1)

In △EBA,

⇒tanβ=

AB

EA

=

EC

h

[∴AB=EC]

⇒EC=

tanβ

h

⟶(2)

From (1)&(2), we get

⇒

tanβ

h

=

tanα

H−h

⇒htanα=Htanβ−htanβ

⇒Htanβ=h(tanα+tanβ)

⇒H=h(1+tanαcotβ)

Hence, the answer is proved.