When the top of a chimney of a factory is seen from a point on the roof of the three storied building of `9sqrt(3)`metre height, the angle of elevation is `30^(@)`. If the distance between the factory and chimney is 30 metres, calculate the height of the chimney.

Explanation

Let AB be the chimney and CD be the building.
CE `bot` AB, `therefore` CE = BD and CD = BE.
As per question, `angleACE = 30^(@)`.
Now, from the right-angled triangle ACE we get
`tan30^(@) = (AE)/(CE)`
or, `(1)/(sqrt(3))= (AE)/(CE) " "or, " "sqrt(3)AE =CE " " or, sqrt(3)AE = BD`
or, ` sqrt(3)AE = 30 " or, AE =(30)/(sqrt(3)) =10sqrt(3)`
Now, AB = AE + BE
` =10sqrt(3) + 9sqrt(3) = 19sqrt(3)`
Hence the height of the chimney = `19sqrt(3)` metres.