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P1 Trigonometry Question

Im stuck on a question from the P1 Textbook, page 247, Question 38, which reads:

" A ship sails 3 nautical miles from P to Q on a bearing 071 degress and then 4 nautical miles from Q to R on a bearing 292 degress. Calculate the distance PR and the bearing of R from P".

I've sketched a litlte diagram, which I think is right, but theres no way of knwing (I dont have a sacnner so I cant scan it and post it here) . I dont know how I would go onto work out the rest of the question, especially part B. Part A, working out the distance, I've tried Sine rule but it doesnt seem to work. Any help would be appreciated.
Reply 1
hint: use the cosine rule for distance PR
Reply 2
El Stevo
hint: use the cosine rule for distance PR


When I use cosine rule, I get a different answer to that ofthe books. Maybe its my diagram. I've attached it .Are there any problems with it?
Reply 3
lemme try again...

heh, method i used was wrong, but the angle fluked right... however, this is the right angle with right reasoning...

the angle you think is 68 is in fact 292-(180+71) = 41 degrees

this is because imagine a north line going through both p and q, then use laws of parallel lines to show that the angle between south and q is 71 degrees, the angle in the triangle is 292-(angle between south and q)-(angle between north and south) = 292-71-180 = 41...
Reply 4
El Stevo
lemme try again...

heh, method i used was wrong, but the angle fluked right... however, this is the right angle with right reasoning...

the angle you think is 68 is in fact 292-(180+71) = 41 degrees

this is because imagine a north line going through both p and q, then use laws of parallel lines to show that the angle between south and q is 71 degrees, the angle in the triangle is 292-(angle between south and q)-(angle between north and south) = 292-71-180 = 41...


Thank you so much for your help, El Stevo. Thanks for taking your time to go through the q. :smile:
Reply 5
no problem :smile: