The angle of elevation of the top of a chimney from the foot of a tower is 60° and the angle of depression of the foot of the chimney from the top of the tower is 30°.If the height of the tower is 40m, find the height of the smoke emitting chimney. According to pollution control norms the minimum height of the smoke emitting chimney should be 100 m.State if the height of the above mentioned chimney meets the pollution norms.What value is discussed in this question.
Answers
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