A house of 15 metres height, stands on one side of a park and from a point on the roof of the house the angle of depression of the foor of chimney of brick kiln of the other side is `30^(@)` and the angle of elelvation of the top of the chimney of brick kiln is `60^(@)` . Find the height of the chimney and the distance between the brick kiln and the house.

Explanation

Let AB be the chimney and CD be the house. The angle of depression of the point B is `30^(@)` and the angle of elevation of the point A io `60^(@)`.
As per question, CD = 15 m.
Let CE is perpendicular to AB. `therefore angleBCE = 30^(@) , " " angleACE = 60^(@)`.
`because " "CE abs() BD, " "therefore " "angleCBD = 60^(@)`.
Now, from the right- angled triangle BCd we get,
`tan 30^(@) = (CD)/(BD)` [ by definition ].
or, `(1)/(sqrt(3)) = (CD)/(BD)`
or, `BD = sqrt(3)CD`
= `sqrt(3)xx15` [ `because` CD = 15 ]
=`15sqrt(3)`.
`therefore BD=CD= 15sqrt(3)`
Again, from the right-angled triangle ACE, we get,
`tan 60^(@) = (AE)/(CE)` [by definition ]
or, `sqrt(3) = (AE)/(15sqrt(3)) [ because " "CE = 15sqrt(3)`metres ]
or, AE = 45
`because " "CE bot AB, " therefore BE = CD = 15` m
Now, AB = AE + BE = (45 + 15 ) m = 60 m.
Hence the height of the chimney = 60 metres and the distance between the brick kiln and the house is `5sqrt(3)` metres.