Question

A vertical tower stands on a horizontal plane and surmounted by a flagstaff of height 'h'. At a point on the plane, the angle of elevation of bottom of the flagstaff is $\alpha$ and that of the top of the flagstaff is $\beta$. find the height of the tower:

• A. $htan\alpha$
• B. $\frac{htan\alpha }{tan\alpha -tan\beta }$
• C. $\frac{htan\alpha }{tan\beta -tan\alpha }$
• D. $\frac{tan\alpha +tan\beta }{htan\alpha }$

Answer 1

The correct option is C $\frac{htan\alpha }{tan\beta -tan\alpha }$

Let the height of tower be 'x' and let the distance of the bottom of the tower from the point on the plane be 'y'.
$tan\alpha =\frac{x}{y}$
$y=\frac{x}{tan\alpha }$ .....(i)
$tan\beta =\frac{x+h}{y}$
$y=\frac{x+h}{tan\beta }$ .....(ii)
From (i) and (ii)
$\frac{x}{tan\alpha }=\frac{x+h}{tan\beta }$
$x(tan\beta -tan\alpha )=htan\alpha$
$x=\frac{htan\alpha }{tan\beta -tan\alpha }$