Two towers 30 m and 90 m high stand on level ground. From the foot of the taller tower the angle of elevation of the top of the shorter one is 30°. The angle of elevation of the top of the taller tower, seen from the foot of the shorter one, is:

The distance between the feet comes from the first sighting: d = 30·cot30° = 30√3 ≈ 52 m. Looking back the other way, tan(elevation) = 90/(30√3) = 3/√3 = √3, so the angle is 60°. The two angles are not equal — the return sighting is steeper because the tower being looked at is three times as tall — so simply copying 30° is the trap.