Convert the following \(\mathrm{RB}\) to \(\mathrm{WCB}\) (a) \(\mathrm{N} 32^{\circ} 30^{\prime} \mathrm{E}\) (b) \(\mathrm{S} 42^{\circ} 40^{\prime} \mathrm{E}\) (c) \(\mathrm{S} 60^{\circ} 30^{\prime} \mathrm{W}\) (d) \(\mathrm{N} 72^{\circ} 50^{\prime} \mathrm{W}\)

Short Answer

Expert verified
Question: Convert the following Relative Bearings to Whole Circle Bearings: (a) N 32°30’ E (b) S 42°40’ E (c) S 60°30’ W (d) N 72°50’ W Answer: (a) WCB = 32°30' (b) WCB = 137°20' (c) WCB = 240°30' (d) WCB = 287°10'

Step by step solution

01

Case (a): N 32°30’ E

To convert N 32°30’ E to WCB, we start at North and move 32°30’ towards East in a clockwise direction. There's no need to do any calculations in this case, as the WCB is the same as the given RB. So, the WCB is 32°30’.
02

Case (b): S 42°40’ E

To convert S 42°40’ E to WCB, we start at South (which is 180° from North) and move 42°40’ towards East in a clockwise direction. We calculate the WCB as follows: \(\text{WCB} = 180° - 42°40'\) \(\text{WCB} = 137°20'\)
03

Case (c): S 60°30’ W

To convert S 60°30’ W to WCB, we again start at South (180°) and move 60°30’ towards West in a clockwise direction. We calculate the WCB as follows: \(\text{WCB} = 180° + 60°30'\) \(\text{WCB} = 240°30'\)
04

Case (d): N 72°50’ W

ToStr convert N 72°50’ W to WCB, we start at North and move 72°50’ towards West in a clockwise direction. To find the WCB, we subtract the RB from 360 degrees: \(\text{WCB} = 360° - 72°50'\) \(\text{WCB} = 287°10'\) In summary, we have converted the given RB to WCB as follows: (a) \(\mathrm{N} 32^{\circ} 30^{\prime} \mathrm{E}\) → \(\text{WCB} = 32°30'\) (b) \(\mathrm{S} 42^{\circ} 40^{\prime} \mathrm{E}\) → \(\text{WCB} = 137°20'\) (c) \(\mathrm{S} 60^{\circ} 30^{\prime} \mathrm{W}\) → \(\text{WCB} = 240°30'\) (d) \(\mathrm{N} 72^{\circ} 50^{\prime} \mathrm{W}\) → \(\text{WCB} = 287°10'\)

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