Q. 254.4( 53 Votes )

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.

Answer :

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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