Towns P, Q, R are such that bearing of P from Q is 070 degrees. R 10km east of Q, PQ = 5 km.

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Denzel

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This is what I've attempted . In part one, I did the right working and got the wrong answer. ( Obviously it's not the right working then..)So then I tried Cos 20 but can someone help me understand what is Cos 20 and why it works? Is angle P from Q actually 020° ? (i) Ans.= 5.6km
In part 2 I tried ...nonsense. Then I tried 142/2= 71. 90-71 = 19+90= 109 but that was 001 ° off. So.. how? (ii) Ans.= 108°Untitled.png1553780643895.png
 

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Bearings are measured from north, so you marked the 70° in the wrong place in the figure. That angle PQR should be 20° (the angle between 70° and east, 90°); the 70° would have been marked above that angle, from north down to QP.
 
How does Q North = 020° and P North = 160° but the total of P does not = 360° if the answer of R from P is 108°???
 
I can't tell what you are saying. What do "P North = 160°" and "the total of P does not = 360°" mean?

Please repeat your question, using fuller explanations.
 
Sorry. So if Q - North-east, is 020° then P - South-west, is 160° because they are parallel. a°( Q (North East) + b°(South West) inside on a parallel line = 180°
So therefore if the total angle counter clockwise at P is 360° how could R from P = 108°, when P inside the triangle is = 142°?
142+ 160 + 108= 410°
 
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Like DrP, I'm confused at your statements....

Enclose the triangle in a rectangle:
Code: 
A                            P                               B
  


Q                                                            R
Get what I mean?
 
Your 160 is wrong. Angle NQR is 70, not 20, as I said before; so angle NPQ (taking N as the direction north of P) is 180 - 70 = 110. Then 110 + 108 + 142 = 360.
 
Dr.Peterson said:
Bearings are measured from north, so you marked the 70° in the wrong place in the figure. That angle PQR should be 20° (the angle between 70° and east, 90°); the 70° would have been marked above that angle, from north down to QP.
Click to expand...
Oh, No I didn't mark it, came with the pic. I see. That makes more sense...
 
Dr.Peterson said:
Your 160 is wrong. Angle NQR is 70, not 20, as I said before; so angle NPQ
(taking N as the direction north of P) is 180 - 70 = 110. Then 110 + 108 + 142 = 360.
Click to expand...
You mean angle NQP is 70, right?
That's why I suggested the rectangle....makes the 70 obvious...
 
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