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 
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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^2 = a^2 + b^2 - 2ab*cos(88)}}}
{{{c^2 = 15^2 + 26^2 - 2*15*26*cos(88)}}}
{{{c^2 = 225 + 676 - 780*0.0348995}}}
{{{c^2 = 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.