question_answer

A flag-post 20m high standing on the top of a house subtends an angle whose tangent is \[\frac{1}{6}\] at a distance 70 m from the foot of the house. The height of the house is

A) 30 m

B) 60 m

C) 50 m

D) None of these

Correct Answer: C

Solution :

\[\tan \alpha =\tan (\varphi -\theta )\] \[\tan \alpha =\frac{1}{6}=\frac{\frac{20+h}{70}-\frac{h}{70}}{1+\frac{(20+h)\,h}{{{(70)}^{2}}}}\] \[\Rightarrow \] \[{{(70)}^{2}}+20h+{{h}^{2}}=(6)(70)(20)\] \[\Rightarrow \] \[{{h}^{2}}+20h+70(70-120)=0\] \[\Rightarrow \] \[{{h}^{2}}+20h-(50)\,(70)=0\] \[\Rightarrow \] \[h=\frac{-20\pm \sqrt{400+(4)(50)(70)}}{2}=50m\].