Question

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​

Answer 1

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.