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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