Question

Two points $AandB$ are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are ${60}^{o}and{45}^o$ respectively. If the height of the tower is $15m$, then find the distance between these points.

Answer 1

REF.Image.

let the distance between C & D is x m

In $△ABC,$

$tan{60}^{\circ }=\frac{AB}{BC}$

$\sqrt{3}=\frac{15}{BC}\Rightarrow BC=5\sqrt{3}m...\left(1\right)$

Now, in $△ABD$

$tan{45}^{\circ }=\frac{AB}{BD}$

$1=\frac{15}{BD}=BD=15m...\left(2\right)$

From (1) & (2),

$x=CD=BD-BC$

$=15-5\sqrt{3}$

$=5\sqrt{3}(\sqrt{3}-1)m$