PLEASE show all calculation steps An instrument is set up over station Stn1, ref

Question

PLEASE show all calculation steps

An instrument is set up over station Stn1, reference Stn2 is sighted and the horizontal circle reading is set to zero. Horizontal circle readings, zenith angles and slope distances are then recorded to points P, Q, R, S. All relevant information/ measurements are recorded in Table Q6. Stn1 1842.482mE, 1739.263mN, 71.378mAOD Stn2 1859.781mE, 1698.283mN Height of instrument 1.529nm Horizontal circle reading 0° 00' 00" 37° 19' 27" 115° 20' 24" 246° 44' 04" 281° 38' 10" Point Zenith angle Slope distance Target height Stn2 89° 06' 26" 89° 38' 18" 92° 08' 50" 91° 48' 31" 37.831 47.713 23.741 29.472 1.300 1.300 1.460 0.400 Fig. Q6 Calculate the bearing of Stn1 to Stn2. Calculate the bearings from Stn1 to points P, Q, R, S. Calculate the horizontal distances from Stn1 to points P, Q, R, S Calculate the coordinates of P, Q, R, S Draw a plan of Stn1, Stn2, P, Q, R, S to scale. Calculate the reduced levels of P, Q, R,;S

Explanation / Answer

Difference in northings of the two stations = 1739.263-1698.283 m = 40.98 m

Difference in eastings of the two stations = 1842.482 - 1859.781 m = - 17.299 m

Let be the angle between the line joining Station 1 & Station 2 with the horizontal X axis.

= tan-1(40.98/-17.299) = -67.11°

Therefore Bearing of Stn1 to Stn2 = (67.11+ 90) + 180 degree = 337.11° = 337°6'36"

Bearing from Stn1 to point P = 337°6'36" + 37°19'27" = 374°26'3"

Bearing from Stn1 to point Q = 337°6'36" + 115°20'24" = 452°27'0" i.e. (452°27'0" - 360°0'0") = 92°27'

Bearing from Stn1 to point R = 337°6'36" + 246°44'04" = 583°50'40" i.e.(583°50'40" - 360°0'0")= 223°50'40"

Bearing from Stn1 to point S = 337°6'36" + 281°38'10" = 618°44'46"

Easting of P = sin374°26'3" x

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