Inclined Stadia Sights

We were solved the problem to get the Inclined Stadia Sights. The Inclined Stadia Sights have the formula of the followings:
ID = Ks Cos oC + C
HD = Ks Cos² oC + C Cos oC
VD = Ks Sin oC Cos oC + C Sin oC
DE = HI + VD – RR

ID = the inclined or slope distance from the center of the instrument (O) to the horizontal cross hair readings (P).
HD = horizontal distance between the instrument and the rod.
VD = vertical distance between the telescope axis (O) and the horizontal cross hair readings (P).
DE = difference in elevation between the instrument station @ m and the distant stadia point @ N.
HI or OM = is the height of the instrument.

Problem:
The following data were obtained by a stadia measurement; vertical angle is 30°23’, and observed stadia intercept is 2.20m. The stadia interval factor at the measurement used 95.50m and C is 0.30m, if the height of the instrument is 1.62m, and the rod reading is taken 1.95m. Determine the HD, VD, ID, and DE.
Given:
K= 95.5m
S= 2.2m
C = 0.3m
Vertical Angle = 30°23’
Solution:
ID = Ks Cos oC + C
= 95.5(2.2) Cos30°23’ + 0.3
= 210.1(0.863) + 0.3
= 181. 32 + 0.3
= 181.62
HD = Ks Cos² oC + C Cos oC
= 95.5(2.2) Cos²30°23’ + 0.3 Cos30°23’
= 210.1(0.863) ² + 0.3(0.863)
= 210.1(0.745) + 0.258
= 156.52 + 0.258
= 156.78
VD = Ks Sin oC Cos oC + C Sin oC
= 95.5(2.2) Sin30°23’ Cos²30°23’ + 0.3 Sin30°23’
= 210.1(0.506) (0.863) + 0.3(0.506)
= 210.1(0.437) + 0.152
= 91.814 + 0.152
= 91.97
DE = HI + VD – RR
= 156.78 + 91.97 - 91.97
= 156.78

We learned this inclined stadia sights to solve the problem to get HD, VD, ID, and DE with the following formulas:
ID = Ks Cos oC + C
HD = Ks Cos² oC + C Cos oC
VD = Ks Sin oC Cos oC + C Sin oC
DE = HI + VD – RR