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Question

The height of a transit station has been computed from the measurement of a slope distance L = 279.1 ± 0.06 m and of a vertical angle α=3o20±30", the probable error in the calculated elevation of station A (in cm) is _______.

A
± 5.4
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B
±6.2
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C
±2.4
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D
±3.6
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Solution

The correct option is A ± 5.4
H=LsinαdHdL=sinα=sin3020
dHdα=Lcosα=279.1×0.9983=278.6255

eH=(eLdHdL)2+(eαdHdα)2

=(0.6×sin3o20)2+(0.000148×278.6255)2

=±0.054 m5.4 cm

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