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# A submarine is being followed by two ships, A and B, 3.8km apart, with A due east of B....

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A submarine is being followed by two ships, A and B, 3.8km apart, with A due east of B. If A is on a bearing of 165 degrees from the submarine and B is on a bearing of 205 degrees from the submarine, find the distance from the submarine to both ships.

The answer is 5.7km and 5.4km

Posted by tamanim on August 31, 2013 at 1:28 AM via web and tagged with math, problems invovling bearings, trigonometry

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Given `AB=3.8` Km (please refer to the attached image)

Since, `ltNSA=165^o` , then `ltESA=ltA=75^o`

Since, major`ltNSB` `=205^o` , <ASB=`40^o`

In `Delta BSA` , `ltB=(180-40-75)=` `65^o`

Applying law of sines we get:

`a/sin75^o=3.8/sin40^o`

`rArr a=5.710312527`

Again, `b/sin65^o=3.8/sin40^o`

`rArr b=5.357865551`

Therefore, A to S`~~` 5.4 Km and B to S`~~` 5.7Km.

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Posted by llltkl on August 31, 2013 at 3:53 AM (Answer #1)