A ladder leaning against a wall makes an angle of 60° with the ground. If the length of the ladder is 19 m, then what is the distance of the foot of the ladder from the wall?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 9.5 m
The ladder, the wall and the ground form a right-angled triangle, with the right angle where the wall meets the ground and the ladder as the hypotenuse. The distance of the foot from the wall is the side next to the 60° angle, so cosine links it to the length of the ladder.
Cosine of the angle at the foot: \(\cos60^\circ=\displaystyle\frac{\text{distance from the wall}}{\text{length of the ladder}}\)
Distance from the wall: \(19\times\cos60^\circ=19\times\displaystyle\frac{1}{2}=9.5\) m