the angle of elevation of the top of a chimney from the foot 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 tower is 40 m, find the height of smoke emitting chimney.
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
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