Two towers, 40 m and 60 m high, stand on level ground. A man standing between them, on the line joining their feet, sees the top of the shorter tower at an elevation of 45° and the top of the taller one at an elevation of 30°. The distance between the two towers is:

The man is 40·cot45° = 40 m from the shorter tower and 60·cot30° = 60√3 ≈ 103.9 m from the taller one. Because he stands between them the two distances add, giving 40 + 60√3 ≈ 143.9 m. Subtracting them would put both towers on the same side of him, and 100 m is just the sum of the two heights, which has nothing to do with the ground distance.