A chimney of 20 m height standing on the top of a building subtends an angle whose tangent is 1/6
at a distance of 70 m from the foot of the building then the height of building is
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Given:
Height of the building is 20m
Distance between the point from foot of the building is 70m.
To Find:
Height of the building.
Solution:
1) Consider the diagram to solve the problem.
- tanX= 1/6
- tanY= h/70
- tanZ=h+20 /70
- Z=X+Y
- tanZ= tanY+tanX /1−tanYtanX
- h+20 /70 = (1/6+h/70)/(1-h/420)
- h+20/70 = (70+6h)/(420-h)
- (20+h)(420-h) = 70(70+6h)
- 8400-20h+420h-h² = 4900+420h
- h²+20h-3500 = 0
- h²+70h-50h-3500=0
- h(h+70)-50(h+70) = 0
- (h+70)(h−50)=0
2)We will consider the positive value as the height can't be negative so h=50m.
Height of the building is 50m.
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