Question

The angle of elevation of the top of the chimney from the foot of a tower is 60 and the angle of depression of foot of chimney from top of tower is 30. if the height of the tower is 40 m . 1)find the height of chimney . 2)according to pollution control norms , the minimum height of smoke emitting chimney should be 100 m . state if the height of the above mentioned chimney meets the pollution norms . 3)what value is discussed in this question?

Answer 1

height of the chimney =CD=h=120m
it meets polution norms

Answer 2

Given : the angle of elevation of the top of a chimney from the top of a tower is 60 degree and the angle of depression of the foot of the chimney from the top of the tower is 30 degree. if the height of the tower is 40m

To find : height of the chimney

Solution :

Tower height = 40 m

Let say chimney Height = H m

Chimney height above tower = H - 40 m

Horizontal Distance between tower & chimney = D m

angle of elevation of the top of a chimney from the top of a tower is 60°

=> Tan 60 = (H - 40)/ D

=> √3 = (H - 40)/ D

=> D√3 = H - 40

angle of depression of the foot of the chimney from the top of the tower is 30°

=> Tan 30 = 40/D

=> 1/√3 = 40/D

=> D = 40√3

=> D√3 = 120

H - 40 = 120

=> H = 160

Chimney height = 160 m

120 m above tower height

Meetings the pollution Norms

Meetings the pollution NormsHence obeying the law & environment friendly