Question

a window of house is 2m above the ground. from the window the angle of elevation and depression of top and bottom of another house situated on the opposite side of the lane are found to be 60 and 45. find the height​

Answer 1

Answer:

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