Exam

NTA Abhyas

Year

2020

Subject

Mathematics

Chapter

Heights and Distances

NTA Abhyas 2020 · Mathematics · Heights and Distances

A chimney of 20 m height standing on the top of a building subtends...

A chimney of $\text{20 m}$ height standing on the top of a building subtends an angle whose tangent is $\dfrac{1}{6}$ at a distance of $\text{70 m}$ from the foot of the building, then the height of building is

Step-by-step solution

Given,& $tan \alpha = \dfrac{1}{6}$

$\tan \left(\alpha + \beta\right) = \dfrac{tan \alpha + tan \beta}{1 - tan \alpha tan \beta}$

$\dfrac{h + 20}{70} = \dfrac{\dfrac{1}{6} + \dfrac{h}{70}}{1 - \dfrac{1}{6} ⋅ \dfrac{h}{70}}$

$\dfrac{h + 20}{70} = \dfrac{70 + 6h}{420 - h}$

$⇒h = 50$

Hence, $\text{50 m}$ is correct choice.