How do you use the law of cosines or law of sines if you are given a = 4, b = 3 and c = 6?

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Answer 1 · 2015-06-20T21:25:44

You can use the Law of Cosines to calculate the angles of the triangle.

#A~~36.3# degrees
#B~~117.3# degrees
#C~~26.4# degrees

In this case the only thing you need to solve this triangle is to calculate the angles.

To calculate angle #A# you use:

#a^2=b^2+c^2-2*b*c*cosA#
so you calculate:

#4^2=3^2+6^2-2*3*6*cosA#
#16=9+36-36cosA#
#36cosA=9+36-16#
#36cosA=29#
#cosA=29/36#
#A~~36.3# degrees

The same way you can calculate C

#c^2=a^2+b^2-2*a*b#
#6^2=3^2+4^2-2*3*4*cosC#
#36=9+16-24cosC#
#36-9-16=-24cosC#
#11=-24cosC#
#cosC=-11/24#
#C~~117.3# degrees.

Now you can calculate B either using the Law of Cosines again or using the fact, that the sum of angles in triangle equals to 180 degrees.

#A+B+C=180#
#36.3+B+117.3=180#
#B=180-117.3-36.3#
#B~~26.4#