A chimney 20 metres high standing on the top of a building subtends an angle whose tangent is 1/6 at a distance 70 metres from the foot of the building. The height of the building is

50 m

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40 m

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60 m

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None

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Solution

The correct option is A $50 m$
$α = θ + β$
tan $θ$ = $\frac{1}{6}$ , tan $α$ = $\frac{(H + 20)}{70}$ , tan $β$ = $\frac{H}{70}$

tan $α$ = $\frac{t a n α + t a n β}{1 - t a n θ t a n β}$

$H^{2}$ + $20 H - 3500 = 0$
or $(H - 50) (H + 70) = 0$
$H = 50, H = - 70$

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A chimney 20 metres high standing on the top of a building subtends an angle whose tangent is 1/6 at a distance 70 metres from the foot of the building. The height of the building is

The correct option is A 50mα=θ+βtan θ = 16, tan α = (H+20)70, tan β = H70tan α = tanα+tanβ1−tanθtanβH2 + 20H−3500=0or (H−50)(H+70)=0H=50,H=−70

The correct option is A $50 m$
$α = θ + β$
tan $θ$ = $\frac{1}{6}$ , tan $α$ = $\frac{(H + 20)}{70}$ , tan $β$ = $\frac{H}{70}$

tan $α$ = $\frac{t a n α + t a n β}{1 - t a n θ t a n β}$

$H^{2}$ + $20 H - 3500 = 0$
or $(H - 50) (H + 70) = 0$
$H = 50, H = - 70$