Question

At a point A, the angle of elevation of a tower of a lower is such that its tangent is $\frac{5}{12};$ on walking 120 meters nearer the tower the tangent of the angle of elevation is $\frac{3}{4}.$ The height of the tower is :

• A. 225 meters
• B. 200 meters
• C. 230 metres
• D. None of these

Answer 1

The correct option is A 225 meters

Here AB is the tower, it is given that

$\tan \varphi =\frac{5}{12}$ ……….(i)

On walling $240$m near to tower, it reaches point C, then $\tan \theta =\frac{3}{4}$ ………(ii)

Let $BC=x$m, $AB=y$m

Now in $\Delta$ABC, $\tan \theta =\frac{y}{x}=\frac{3}{4}$

$\Rightarrow x=\frac{4}{3}y$

Now $\tan \theta =\frac{y}{240+x}=\frac{5}{12}$

$=\frac{y}{240+\frac{4}{3}y}=\frac{5}{12}$

$\Rightarrow 12y=1200+\frac{20}{3}y$

$\Rightarrow 36y-20y=3600$

$\Rightarrow 16y=3600$

$\Rightarrow y=225$m.