How do you solve the triangle when given a=5, b=7, and c=6?

1 Answer
Alan P.
Nov 28, 2015

Use the Law of Cosines to determine the angles

Explanation:

Law of Cosines
#color(white)("XXX")c^2=a^2+b^2-2abcos(/_C)#
#rArr#
#color(white)("XXX")cos(C) = (a^2+b^2-c^2)/(2ab)#

Similarly
#color(white)("XXX")cos(A) = (b^2+c^2-a^2)/(2bc)#
and
#color(white)("XXX")cos(B)= (a^2+c^2-b^2)/(2ac)#

Substituting the given values for #a, b, and c#
we get
#color(white)("XXX")cos(/_A) = 0.714#
then taking the #arccos# of both sides:
#color(white)("XXX")/_A = arcos(0.715) = 0.775 " radians" = 44.4^@#

Similarly we can find:
#color(white)("XXX")/_B = 1.369 " radians" = 78.5^@#
and
#color(white)("XXX")/_C = 0.997 " radians" = 57.1^@#

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