Question

The angle of elevation from a window to the top of a flag is $60^{\circ}$ and the angle of depression to the base of the flag is $30^{\circ}$. The horizontal distance of the window from the flag is 6 m. Then the height of the flag is

• A. $2 \sqrt{3}$ meters
• B. $4 \sqrt{3}$ meters
• C. $8 \sqrt{3}$ meters
• D. $16 \sqrt{3}$ meters

Answer 1

Answer: (C)

Let $AB =$ height of flag

In $ΔBDC$,
$tan \,60^{\circ} = \frac{BD}{CD}$
$ BD = 6\sqrt{3} $
In $Δ ACD$,
$ tan \,30^{\circ} = \frac{AD}{CD} $
$\Rightarrow AD = \frac{6}{\sqrt{3}} $
Height of flag $ = BD + AD = 6\sqrt{3} + \frac{6}{\sqrt{3}} $
$= 6\sqrt{3} +2\sqrt{3} = 8\sqrt{3} m$