A ladder 10 m long has its foot at a fixed point in a narrow lane in Amritsar. Resting against the wall on one side of the lane it makes an angle of 60° with the ground; turned over to rest against the wall on the other side, it makes an angle of 30° with the ground. Find the exact width of the lane (in m).

Question

Accepted Answer

5(√3 + 1). Foot to the first wall: 10 cos 60 = 5 m. Foot to the second wall: 10 cos 30 = 5 √3 m. The two walls are on opposite sides of the fixed foot, so the width = 5 + 5 √3 = 5(√3 + 1) m (about 13.66 m). Subtracting instead of adding is the common slip.

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