How do you use the law of cosines or law of sines if you are given a = 4, b = 5, and c = 6?

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Answer 1 · 2015-09-06T11:00:03

You can use the Law of Cosines to find the remaining angles.

If you mark angles as:
$A$ the angle opposite to side $a$
$B$ the angle opposite to side $b$
$C$ the angle opposite to side $c$

Then from the Law of Cosines you have:

$c^2=a^2+b^2-2abcosC$

After substituting you get:

$6^2=5^2+4^2-2*5*4*cosC$

$36=25+16-40cosC$

$40cosC=41-36$

$cosC=1/8$

$C~~82.8 deg$

If you repeat simmilar calculations for $B$ you get:

$cosB=9/16$

$B~~55.77 deg$

Now you can calculate the remaining angle either using the Law of Cosies again or using the property of Sum of Angles in a Triangle

$A+B+C=180$
$A=180-B-C$
$A=180-55.77-82.8$
$A~~41.43deg$