Tuesday, February 23, 2016

For a triangle ABC if C=106.2, a=8.3 and b=11.78, what is c?

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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