The angles of depression of the top and bottom of 8 m tall building from the top of a multistoried building are 30° and 45° respectively. Find the height of the multistoried building and the distance between the two buildings.
Let DC is tall building and AB is multistoried building.
AB = AE+EB
AB = h+8 ----------(1)
In ∆ABC,
tan 45° = 
1 = 
----------(2)
In ∆AED,
tan 30° = 
= 
√3h = 
---------(3)
Substituting value of 
from eqn. (2) in eqn. (1)
√3h-h = 8
h = 
h = 
⇒ 
h = 4(√3+1)m. --------(4)
Substituting value of h from eqn. (4) in eqn. (3)
√3h = 
√3× 4(√3+1)
√3 (4√3+4)
Therefore height of multistoried building is
= 8+4(√3+1)
= 8+4√3+4
= 12+4√3
= 4(3+√3) m.
Distance between two building is 4(3+√3) m.
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