How to calculate bearings from included angles in surveying?/ Finding bearings from included angles in compass surveying.

 Eg:

Find the bearings of all the lines in a closed traverse for the following given data.

The bearing of AB = 67°30'

ㄥA= 134°15', ㄥB= 94°45',  ㄥC= 54°30', &ㄥD= 76°30'.

Calculation:

First, let us draw the closed traverse for the above-given data.

Known concept or formula:

 If FB>180°, then BB = FB-180°

If FB < 180°, then BB = FB +180°

1. Line AB:

FB of line AB = 67°30' (given) < 180°

BB of line AB = [ FB + 180°]

                        = [ 67°30' +180°]

                        = 247°30'

2. Line BC:

As you can observe in the drawing when you deduct the ㄥB from the BB of line AB, you will get FB of line BC.

Therefore 

FB of line BC = [BB of line AB - ㄥB]

                       = [247°30' - 94°45']

                       = 152°45' < 180°

BB of line BC  = [ FB + 180°]

                        = [ 152°45' +180°]

                        = 332°45'

3. Line CD:

FB of line CD = [BB of line BC - ㄥC]

                       = [332°45' - 54°30']

                       = 278°15' > 180°

BB of line CD  = [ FB - 180°]

                        = [ 278°15' -180°]

                        = 98°15'

4. Line DA:

FB of line DA = [BB of line CD - ㄥD]

                       = [98°15' - 76°30']

                       = 21°45' < 180°

BB of line DA  = [ FB + 180°]

                        = [ 21°45' +180°]

                        = 201°45'

Check:

FB of line AB  = [BB of line DA - ㄥA]

                       = [201°45' - 134°15']

                       = 67°30' ✔

Line	FB	BB
AB	67°30'	247°30'
BC	152°45'	332°45'
CD	278°15'	98°15'
DA	21°45'	201°45'

 

To understand A to Z of surveying, click here.

Thank you for going through these calculation steps❤. Have a good day 😄.

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