From a point on level ground 48 m from the foot of a vertical tower, the angle of elevation θ of the top satisfies tanθ = 5/12. The height of the tower is:

Height = 48·tanθ = $48\times 5/12=20$ m. Using cotθ by mistake multiplies by 12/5 and gives 115.2 m, which would make the elevation far steeper than the given ratio allows. The value 52 m is the straight-line distance from the point to the top, √$(48^2+20^2)$ — a 5-12-13 triangle scaled by 4 — and 60 m comes from misreading the ratio as 5/4.