Let AD = monument, with foot at A
P = point of observation
Given AB = a, AC = b, AD = c, AP = x
and α+β+γ = 180°.
From ΔAPB, tanα = a/x
From ΔAPC, tanβ = b/x
From ΔAPD, tanγ = c/x
Since α+β+γ = 180° => S1 = S3
=> tanα + tanβ + tanγ = tanα . tanβ . tanγ
=> x2 (a + b + c) = abc.