How do you find the measure of each of the angles of a triangle given the measurements of the sides are 12, 20, 22?

1 Answer
Dec 6, 2016

Answer:

Use the Law of Cosines as demonstrated below.

Explanation:

Let #/_A# be the angle opposite side #abs(a)=22#
and #/_B# be the angle opposite side #abs(b)=20#
and #/_C# be the angle opposite side #abs(c)=12#

The Law of Cosines tells us that
#color(white)("XXX")abs(a)^2=abs(b)^2+abs(c)^2-2abs(b)abs(c)cos(A)#
or (in a form more useful for this problem):
#color(white)("XXX")cos(/_A)= (abs(b)^2+abs(c)^2-abs(a)^2)/(2abs(b)abs(c))#
or...
#color(white)("XXX")/_A = "arccos"((abs(b)^2+abs(c)^2-abs(a)^2)/(2abs(b)abs(c)))#

Using the given values (and a calculator)
#color(white)("XXX")/_A ~~ 1.445468# (radians)

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Similarly, we can find:
#color(white)("XXX")/_B~~1.124289# (radians)
and
#color(white)("XXX")/_C~~0.571835# (radians)