Question

From the top of a 7m high building, the angle of elevation of top of the cable tower is 60° and the angle of depression of it's foot is 45°. Determine the height of the tower.

• A. $7m$
• B. $\sqrt{3}m$
• C. $(7-7\sqrt{3})m$
• D. $(7+7\sqrt{3})m$

Answer 1

The correct option is D $(7+7\sqrt{3})m$

We know that, AB = CD = 7cm.

From the figure,
$tan45°=\frac{CD}{AD}\Rightarrow 1=\frac{7}{AD}\Rightarrow AD=7m$

Hence, from the triangle ADE,
$tan60°=\frac{ED}{AD}\Rightarrow \sqrt{3}=\frac{ED}{7}\Rightarrow ED=7\sqrt{3}m$

The total height of the cable tower
$=CD+ED=(7+7\sqrt{3})m$