Trigonometric Leveling
1. When the distance D can be measured:

h/D = tanѲ
h = D tanѲ
R.L. of top = R.L. of point A + Height of Instrument (HI) + h
If the distance D is much greater, then we consider the effect of curvature ‘c’

Corrected length, h’ = h – c
R.L. of top = R.L. of point A + Height of Instrument (HI) + h’
2. When the distance D can’t be measured:

TanѲ1 = V/(B+D)
V = B tanѲ1 + D tanѲ1 …………………..(i)
TanѲ2 = V/D
V = D tanѲ2 ………………………………….(ii)
from eqn. (i) and (ii)
we get, D tanѲ2 = B tanѲ1 + D tanѲ1
D tanѲ2 – D tanѲ1 = B tanѲ1
D (tanѲ2 – tanѲ1) = B tanѲ1
Thus, D = B tanѲ1 / (tanѲ2 – tanѲ1)
Also, V = B tanѲ1 tanѲ2 / (tanѲ2 – tanѲ1)
Therefore, R.L. of point P = R.L. of B.M. + B.S. (Back Side) + V + Correction (only applicable if large distance).