The angles of depression of the top and bottom of a 20 m high building from the top of a multistoryed building are 300 and 450 respectively. Find the height of the multistoryed building. (Take root 3 = 1.732)
Let CD be the building with CD = 20m and AB = h m be the height of multistoryed building.
∠CAE = 30° and ∠CBD = 45°
As AB = h m ⇒ CE = (20 – h) m
So in right angled ∆ACE,
In ∆BCD,
⇒CD = BD·1
⇒BD = CD ............(2)
as BD = AE, so from (1) and (2)
Given CD = 20m
⇒ h = 8.45 m
Hence, the height of multistoryed building is 8.45 m.