From a point on the roof of five-storied building the angle of elevation of the top of a monument and that of angle of depression of the foot of the monument are `60^(@) and 30^(@)` respectively. If the height of the building is 16 metres, calculate the height of the monument and the distance of the building from the monument.

Explanation

Let AB be the monument and CD be the building.
`DE bot AB " "therefore` De = BC and CD = BE = 16 m
As per question,
`angleADE = 60^(@) and angleBDE = 30^(@)`
Now, from the right-angled triangle BDE we get,
`tan 30^(@) = (BE)/(DE)` [ by definiton ]
or, `(1)/(sqrt(3)) = (16)/(DE) " " or, " "DE = 16sqrt(3)`............(1)
Again, from the right-angled triangled ADE we get ,
`tan 60^(@) = (AE)/(DE)`
or, `sqrt(3) = (AE)/(16sqrt(3)) " "or, " " AE = 48`
`therefore " " AB = AE + BE = (48 + 16)` m. =64 m.
Hence the height of monument is 64 m. and the distance of the building from the monument is `16sqrt(3)`m.