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#