The top of a straight ladder rests against a vertical wall at a window sill 6 m above the ground, and the ladder makes an angle of \(60^\circ\) with the ground. Find the length of the ladder.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(4\sqrt{3}\) m
The ladder, the wall and the ground form a right-angled triangle with the ladder as the hypotenuse. The 6 m height is the side opposite the \(60^\circ\) angle, so the sine links it with the ladder.
\(\sin 60^\circ=\displaystyle\frac{6}{L}\)
\(L=\displaystyle\frac{6}{\sqrt{3}/2}=\frac{12}{\sqrt{3}}=\frac{12\sqrt{3}}{3}=4\sqrt{3}\) m
