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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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law of cosines: \[c^2 = a^2 + b^2 - 2abcos(\theta)\] c is the longest side, notice that pythagoras' is the special case of law of cosines, where theta = 90. \[165^2 = 83^2 + 111^2 - 2(83)(111)\cos(\theta)\]
you end up with: cos(theta) = 0.434983175 so with your calculator, use the cos^(-1) button on 0.434983175 (cos inverse) to get the obtuse angle: 64.2 degrees the direction north of west would be 180 degrees - 64.2 degrees

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Other answers:

  • phi
yes
  • phi
Re-reading the question, they want the angle "degrees North of West"
  • phi
|dw:1369857679392:dw|
  • phi
Euler lost a minus sign the angle you want plus 115.8 add up to a straight line
  • phi
answer + 115.8 =180 solve for answer
  • phi
I would add -115.8 to both sides
  • phi
yes, the ship was heading west (270 degrees) and it turned 64.2ยบ toward the north.

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