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guti21 · Dec 10, 2009, 03:53 PM

A ship leaves port on a bearing of 34 degrees and travels 10.4 miles. The ship then turns due east and travels 4.6 miles. How far is the ship from the port and what is its bearing from port?
If you can include a picture that would be great thanks.

galactus · Dec 11, 2009, 12:04 PM

Use the law of cosines

To find the distance from where it started to where it ends up.

Due east is a bearing of 90 degrees.

180-(90-34)=124.

$\sqrt{(10.4)^{2}+(4.6)^{2}-2(10.4)(4.6)cos(124)}=13.52$

To find the bearing back to the point of origin, try using the law of sines.

$\frac{sin(A)}{4.6}=\frac{sin(124)}{13.52}$

$A=16.383 \;\ deg$

$34+16.383+180=230.383 \;\ degrees$

That is the bearing heading back to the point of origin.

Follow all that? The best thing is to outline it and ask questions if you do not understand. Draw a picture. That always heps with these. Get a protractor and a rule and draw it out to scale.

nia16 · May 10, 2012, 02:23 PM

The bearings of a ship A from a ship B is 324 degrees.ship C is 8km due north of B and is due east of A.how far is C from A.what is the bearings from Bfrom A.

Stratmando · May 10, 2012, 05:33 PM

Galactus, you are always Great with Math.
How accurate is it if you draw it out?