Since we know two lengths of the sides of triangle ABC and
the angle enclosed by them, then the length of the side c could be evaluated using the
law of cosines.
c^2 = a^2 + b^2 - 2a*b*cos
C
We'll replace a and b by its
values:
c^2 = (8.3)^2 + (11.78)^2 - 2*8.3*11.78*cos
106.2
Since the angle 106.2 is in the 2nd quadrant, the
value of the function cosine is negative.
cos 106.2 =
-0.27
c^2 = 68.89 + 138.76 +
54.55
c^2 = 262.20
c = sqrt
262.20 => c = 16.19
We'll keep only the positive
value since the length of a side cannot be
negative.
Therefore, the requested length of
the side c is c = 16.19 units.
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