Question

$A$ and $B$ are two stations due north and south of a tower of height $25m$. The angles of depression of the stations from the top of the towe $r$ observed to be ${30}^0$ and ${45}^0$ respectively. The distance between the two stations is

• A. $25(\sqrt{3}+1)$
• B. $25(\sqrt{3}-1)m$
• C. $25\sqrt{3}m$
• D. $25(2+\sqrt{3})m$

Answer 1

The correct option is A $25(\sqrt{3}+1)$

$\tan {45}^0=\frac{25}{d_2}$
$d_2=25$
$\tan {30}^0=\frac{25}{d_1}$
$d_1=25\sqrt{3}$
$d_1+d_2=25(\sqrt{3}+1)m.$