A ladder of length 30 m is leaning against a wall making an angle of 30° with the horizontal. Find the distance between the foot of the ladder and the wall.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(15\sqrt{3}\) m
The ladder, the wall and the ground form a right-angled triangle with the ladder as the hypotenuse. The distance from the foot to the wall is the side next to the 30° angle, so it is found with the cosine.
Cosine of the angle at the foot = side next to it ÷ hypotenuse: \(\displaystyle\cos30^\circ=\frac{\text{distance}}{30}\)
Distance from the foot to the wall: \(\displaystyle30\times\frac{\sqrt{3}}{2}=15\sqrt{3}\) m
