## lala2 2 years ago .

1. Euler271

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. $165^2 = 83^2 + 111^2 - 2(83)(111)\cos(\theta)$

2. Euler271

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

3. lala2

@Euler271 ??

4. lala2

@phi ?

5. phi

yes

6. phi

Re-reading the question, they want the angle "degrees North of West"

7. phi

|dw:1369857679392:dw|

8. phi

Euler lost a minus sign the angle you want plus 115.8 add up to a straight line

9. phi

10. phi

I would add -115.8 to both sides

11. phi

yes, the ship was heading west (270 degrees) and it turned 64.2º toward the north.