From the top of a building 30 m high, the angle of depression of the foot of a nearby vertical tower is 60°, and the angle of elevation of the tower's top is 45°. Both stand on the same level ground. The height of the tower is:

The depression of the tower's FOOT fixes the horizontal gap: d = 30·cot60° = 30/√3 = 10√3 ≈ 17.32 m. Looking up at 45° across that gap puts the tower's top d·tan45° = 10√3 above the roof, so the tower measures 30 + 10√3 ≈ 47.32 m from the ground. Stopping at 10√3 reports only the part poking above the roof and forgets the building's own 30 m. Swapping the two angles — using the depression 60° for the top and the elevation 45° for the foot — gives d = 30 and hence 30 + 30√3 ≈ 82.0 m, while 30√3 ≈ 52.0 m uses the wrong ratio for the gap.