Answer Happy

The height of a new point P was determined from five existing
benchmarks A, B, C, D, E by using the levelling survey, see the
survey
scheme.
From the benchmarks with given heights (HA ,
HB , HC , HD ,
HE) five levelling lines were run with observed height
differences: ∆hAP , ∆hBP ,
∆hCP , ∆hDP and
∆hEP to determine the height of the point P.
The accuracy of levelling is given in terms of variances of
levelling height differences
(σAP2 , σBP2, σCP2 , σDP2 and σEP2).
The measurements and variances are summarized in the table.
Height of benchmark [m]
Height difference [m]
variance [cm]
HA = 3.520 m
∆hAP = 3.475 m
σAP2 = 1 cm2
HB = 4.813 m
∆hBP = 2.227 m
σBP2 = 3 cm2
HC = 5.766 m
∆hCP = 1.196 m
σCP2 = 2
cm2
HD = 5.671 m
∆hDP = 1.234 m
σDP2 = 1 cm2
HE = 4.667 m
∆hEP = 2.238 m
σEP2 = 1 cm2
The result is?
Y