Calculating internal angles and bearing of triangle

[Geodan]

Hi there,

Would appreciate any help / clarification on this problem.

Problem:
Man walks 7km at bearing 024 from O to A, then walks 2km at bearing 160 from A to B. Find distance OB and bearing of O from B.

I have worked out that OB is 5.73km (cosine rule) but for the bearing I keep getting 218.03 and the answer in textbook gives 282 and I cannot see how. My internal angles are 14.03, 44 & 121.97 - these seem to align with expectation if I draw it out to scale.

Again, any clarification on what I have missed is much appreciated.

 

[Deleted member 4993]

Hi there,

Would appreciate any help / clarification on this problem.

Problem:
Man walks 7km at bearing 024 from O to A, then walks 2km at bearing 160 from A to B. Find distance OB and bearing of O from B.

I have worked out that OB is 5.73km (cosine rule) but for the bearing I keep getting 218.03 and the answer in textbook gives 282 and I cannot see how. My internal angles are 14.03, 44 & 121.97 - these seem to align with expectation if I draw it out to scale.

Again, any clarification on what I have missed is much appreciated.

I get the textbook answer:

360 - (58.026 + 20) = 281.97

 

[Geodan]

I get the textbook answer:

360 - (58.026 + 20) = 281.97

Thanks for your comment. Using the sine rule that (58.026) is what I estimated originally, but then I struggled to balance the internal angles of the triangle to 180. If I use the sine rule for the smallest angle first (AOB), as to avoid issues with number greater than 90, that gives me 14.03. You are then left with a much larger angle for OAB. When scaled out this makes more sense.


Happy to know your thoughts on it.

 

[Harry_the_cat]

Thanks for your comment. Using the sine rule that (58.026) is what I estimated originally, but then I struggled to balance the internal angles of the triangle to 180. If I use the sine rule for the smallest angle first (AOB), as to avoid issues with number greater than 90, that gives me 14.03. You are then left with a much larger angle for OAB. When scaled out this makes more sense.


Happy to know your thoughts on it.

Labelling the triangle OAB in the usual way, Angle O = 14.03 (as you said ... smallest angle opposite smallest side), Angle A = 44 and Angle B = 180 - (44 + 14.03) = 121.97.

The bearing from B to O is therefore 160 + (180 - 121.97) = 218.03.

As you've said, and a diagram clearly shows, that the bearing could not possibly be larger than 270.

I believe the book's answer is incorrect.

 

[Geodan]

Labelling the triangle OAB in the usual way, Angle O = 14.03 (as you said ... smallest angle opposite smallest side), Angle A = 44 and Angle B = 180 - (44 + 14.03) = 121.97.

The bearing from B to O is therefore 160 + (180 - 121.97) = 218.03.

As you've said, and a diagram clearly shows, that the bearing could not possibly be larger than 270.

I believe the book's answer is incorrect.

Thanks for the comment, it is what I was thinking - something did not seem right.

 

[Deleted member 4993]

Thanks for your comment. Using the sine rule that (58.026) is what I estimated originally, but then I struggled to balance the internal angles of the triangle to 180. If I use the sine rule for the smallest angle first (AOB), as to avoid issues with number greater than 90, that gives me 14.03. You are then left with a much larger angle for OAB. When scaled out this makes more sense.


Happy to know your thoughts on it.

You are correct. I forgot the second solution of sin^-1(x) which is 180°-Θ. So the angle should be 180 - 58.0264 = 121.9736° and your answer is correct (and the book made similar mistake as I did and is incorrect). Never hire me as a guide in wilderness!!