Question

A ladder of a fire truck is elevated to an angle of ${60}^{\circ }$ and extended to a length of $70feet$. If the base of the ladder is $7feet$ above the ground, how many feet above the ground does the ladder reach?

• A. $35ft$
• B. $42ft$
• C. $35\sqrt{3}ft$
• D. $7+35\sqrt{3}ft$
• E. $7+42\sqrt{3}ft$

Answer 1

The correct option is D $7+35\sqrt{3}ft$

In $△BAC,$

$\sin 60°=\frac{BC}{AB}=\frac{BC}{70}$

$\Rightarrow \frac{\sqrt{3}}{2}=\frac{BC}{70}$

$\Rightarrow BC=\frac{70\sqrt{3}}{2}$

$\Rightarrow BC=35\sqrt{3}$

$\therefore$ The ladder reaches $(7+35\sqrt{3})m$ above the ground.

Hence, the answer is $(7+35\sqrt{3}).$