Question

Point A : (93.00E, 662.00N)
Point B : (686.525E, 470.662N)
Angle observed at A from B to C 46 050′04"
Horizontal distance AC : 478m
Angle observed at B from A to D 85039′00"
Horizontal distance BD : 273m
1. From the measurements made on site (above), calculate the distance between points C
and D.
2. Given that the angle observed at A from B to D is 25010′20" carry out an independent
mathematical check on the co-ordinates of D.
3. Estimate the standard error of the point C if the measured distances have a standard
error of +/- 8mm and the observed angles +/- 15”

Answer 1

Hi,

Solution as follows:

Please refer to the attached sketch for better understanding:

QUESTION 1: DISTANCE BETWEEN C AND D

Step 1: Calculating azimuth of each line

Azimuth of AC (α_AC) = 107ᵒ52’05” – 46ᵒ50’04” = 61ᵒ02’01”

Azimuth of BD (α_BD) = 107ᵒ52’05” + 85ᵒ39’00” +180^o = 373ᵒ31’05” = 13ᵒ31’5”

Step 2: Calculating latitude and departure of AC and BD

Latitude of a line = L cosα

Departure of a line = L sinα

Where, L = Length of line and α = Azimuth

Accordingly the results are calculated in table below:

Line	Azimuth	Length (ft)	Latitude (m)	Departure (m)
AC	61ᵒ02’01”	478.000	231.494	418.204
BD	13ᵒ31’5”	273.000	265.437	63.814

Step 3: Calculating coordinates of C and D

North coordinate of a point over line = North coordinate of start point + Latitude

East coordinate of a point over line = East coordinate of start point + Latitude

Accordingly the results are calculated in table below:

Line	Station	Latitude	Departure	Northing	Easting
	A			662.000	93.000
AC		231.494	418.204
	C			893.494	511.204
	B			470.662	686.525
BD		265.437	63.814
	D			736.099	750.339

Step 4: Calculating length of line CD from site measurements:

Hence distance between C and D,

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