Question

A flagstaff $20m$ high standing on the top of a house subtends an angle whose tangent is $1/6$ at a distance $70m$ 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

Answer 1

Answer: (C)

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