From a point on level ground the angle of elevation of the top of a tower is 45°. On walking 20 m straight towards the tower the elevation becomes 60°. The height of the tower is:

If the tower is h m high, the two standpoints are h·cot45° = h and h·cot60° = h/√3 from its foot, and the 20 m walk is the difference: h − h/√3 = 20. So h(√3 − 1) = 20√3 and h = 20√3/(√3 − 1) = 20√3(√3 + 1)/2 = 10(3 + √3) ≈ 47.3 m. (Check: 47.3 and 27.3 differ by 20.) Rationalising with the wrong conjugate gives 10(3 − √3) ≈ 12.7 m, far too short for a 20 m walk to swing the sighting from 45° to 60°.