SOLUTION: A man start from P and walk 8km on a bearing of 70 degree. He then walk 12km on the bearing of 105 degree to Q, what is the bearing of Q from P
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Question 1140526: A man start from P and walk 8km on a bearing of 70 degree. He then walk 12km on the bearing of 105 degree to Q, what is the bearing of Q from P Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Draw this.
We know two side lengths and the angle between, which is 145 degrees. Call that side c and use Law of Cosines
c^2=a2+b^2-2abcos C
=64+144-2*8*12(-0.819)
=208+157.24
=365.24
c=sqrt(365.24)=19.11 km
Now use Law of Sines
19.11/sin 145=12/sin A, where A is the angle between the original direction walked and the final bearing.
33.32=12/sin A
sin A=12/33.32=0.3601
sin^-1 of 0.3601=21.11 degrees.
That is measured from the 70 degree bearing first started, so the final bearing is 91.11 deg
