Question

A tower subtends an angle of 30$^\circ$ at a point on the same level as the foot of the tower. At a second point h metres above the first, the depression of the foot of the tower is 60$^\circ$. The horizontal distance of the tower from the point is.

• A. $h$ cot 60$^\circ$
• B. $h$ cot 30$^\circ$
• C. $\frac {h} {3}$ cot $60^\circ$
• D. $\frac {h} {3}$ cot $30^\circ$

Answer 1

Answer: (A)

$h$ cot 60$^\circ$

Answer 2

Let PQ = $x$ metres denote the tower so that $\Delta PAQ = 30^\circ$. Let AB = $h$ metres. $\therefore \, \Delta BQA = 60^\circ$ Now, $\frac{h}{AQ}$ = tan $60^\circ = \sqrt{3}$ $\therefore$ AQ = $\frac{h}{\sqrt{3}} = h$ cot $60^\circ$