Question

A man of height $6$ ft. observes the top of a tower and the foot of the tower at angles of ${45}^{\circ }$ and ${30}^{\circ }$ of elevation and depression respectively. Assuming the man to stand on the level ground, the height of the tower is :-

• A. $6\left(\sqrt{3}-1\right)ft.$
• B. $6\left(\sqrt{3}+1\right)ft.$
• C. $6\left(\sqrt{2}-1\right)ft.$
• D. None of these

Answer 1

Answer: (B)

$6\left(\sqrt{3}+1\right)ft.$

$InABC$

$\tan {30}^0=\frac{AB}{BC}$
$\frac{1}{\sqrt{3}}=\frac{6}{BC}$
$BC=6\sqrt{3}$
$AD=6\sqrt{3}\left(BC=AD\right)$

$NowinADE$
$\tan {45}^0=\frac{ED}{AD}$
$1=\frac{ED}{6\sqrt{3}}$
$ED=6\sqrt{3}$
$h=ED+DC$
$=6\sqrt{3}+6$
$=\left(6\sqrt{3}+1\right)$ft