The angle of elevation of the top of a chimney from the foot of a tower is60 and the angle of depression of the foot of the chimney from the top ofthe tower is 30. If the height of the tower is 40 m, find the height of thechimney. According to pollution control norms, the minimum height of asmoke emitting chimney should be 100 m. State if the height of theabove mentioned chimney meets the pollution norms. What value isdiscussed in this question ?is the answer 120mjust a yes or no will do, no similar queries
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The angle of elevation of the top of a chimney from the foot of a tower is60 and the angle of depression of the foot of the chimney from the top ofthe tower is 30. If the height of the tower is 40 m, find the height of thechimney?
The angle elevation of chimney=60°
The angle of depression tower to the foot of chimney or angle of elevation of tower from foot of the chimney=30°.
Now in tower,
H=40m
So,
Cot30°= adj÷opp
√3=adj÷40
Therefore,
adj=40√3m. (opp is H of the tower)
Now in chimney,
Tan60°=opp÷adj
√3=opp÷40√3
opp= 40√3×√3
opp= 120m (opp is H of chimney)
Therefore,
H of chimney is 120m.
The angle elevation of chimney=60°
The angle of depression tower to the foot of chimney or angle of elevation of tower from foot of the chimney=30°.
Now in tower,
H=40m
So,
Cot30°= adj÷opp
√3=adj÷40
Therefore,
adj=40√3m. (opp is H of the tower)
Now in chimney,
Tan60°=opp÷adj
√3=opp÷40√3
opp= 40√3×√3
opp= 120m (opp is H of chimney)
Therefore,
H of chimney is 120m.
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