A vertical tower stands on the horizontal ground and is surmounted by a vertical flagstaff of height 'h' metre. At a point on the ground, the angle of elevation of the bottom of the flagstaff is $α$ and that of the top of the flagstaff is $β$ . The height of the tower is ___ m.

$h t a n α$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{h t a n α}{t a n β + t a n α}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{t a n α}{t a n β - t a n α}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{t a n α}{t a n β - t a n α}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D
$\frac{t a n α}{t a n β - t a n α}$

Let the height of the tower be 'x' and the distance of the point from the bottom of the tower be 'y'.

In $Δ A B D$

$t a n α = \frac{x}{y}$

$y = \frac{x}{t a n α}$ ....... (i)

In $Δ A C D$

$t a n β = \frac{x + h}{y}$

$t a n β = \frac{x + h}{\frac{x}{t a n α}}$

$t a n β = \frac{(x + h) t a n α}{x}$

$∴ x t a n β = x t a n α + h t a n α$

$x (t a n β - t a n α) = h t a n α$

$x = \frac{h t a n α}{t a n β - t a n α}$

Suggest Corrections

Similar questions

α

β

(\frac{h t a n α}{t a n β - t a n α})

α

β

α a n d β

\frac{h tan α}{tan β - tan α}

Join BYJU'S Learning Program