SOLUTION: From a lighthouse L an aircraft carrier A is 15km away on a bearing of 112 degrees and a submarine S is 26 km away on a bearing of 200 degrees. Find a) the distance between A a

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Question 155862: From a lighthouse L an aircraft carrier A is 15km away on a bearing of 112 degrees and a submarine S is 26 km away on a bearing of 200 degrees. Find
a) the distance between A and S
b) the bearing of A from S
Please I need desperate help...its due later today!!!!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
From a lighthouse L an aircraft carrier A is 15km away on a bearing of 112 degrees and a submarine S is 26 km away on a bearing of 200 degrees. Find
a) the distance between A and S
b) the bearing of A from S
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Sketch it, and you'll see that the angle ALS is 88 degs (200 - 112).
Use the law of cosines to find side AS.
c%5E2+=+a%5E2+%2B+b%5E2+-+2ab%2Acos%2888%29
c%5E2+=+15%5E2+%2B+26%5E2+-+2%2A15%2A26%2Acos%2888%29
c%5E2+=+225+%2B+676+-+780%2A0.0348995
c%5E2+=+873.778...
c = 29.5597 (distance AS)
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Now find the angle LAS by the law of sines
sin(LAS)/26 = sin(88)/29.5597
Angle LAS = 61.53 degs
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The heading from the AC to the Lighthouse is 112 + 180 = 292
Subtract 61.53 from that, for a heading of
230.47, just slightly west of southwest.