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# law of cosines

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whats 400=169+121-286CosC . i keep getting 74.something and the answer is 112degrees37seconds? i can't find my calculator
Jan 30, 2012

#1
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112.61986494804282480511 is what I come up with. Not sure how many decimals you need to round to, but that's it.

my final equation was:

C=acos((169+121-400)/286)
Jan 30, 2012
#2
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$$400 = 169 + 121 - 286\cos C\\ -286\cos C = 400 - 169 - 121\\ \cos C = -\dfrac{110}{286}\\ C = 112.6198649^{\circ} = 112^{\circ}37'11.51''$$

the arccosine of a negative number is in the range 90° < x $$\leqslant$$ 180°

Aug 21, 2016