The sum of the angles of a triangle is equal to 180 degrees.
We have then:
[tex] A + B + C = 180
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From here, we clear C:
[tex] C = 180 - A - B
[/tex]
Substituting values:
[tex] C = 180 - 23 - 48
C = 109 [/tex]
We now look for the lontigudes of the sides.
To do this, using the sines law we have:
[tex] \frac{c}{sine (109)} =\frac{14}{sine (23)}
[/tex]
From here, we clear c:
[tex] c =\frac{14}{sine (23)}*sine(109)
[/tex]
[tex] c = 33.88
[/tex]
We repeat the same procedure for b:
[tex] \frac{b}{sine (109)} = \frac{14}{sine (23)}
[/tex]
[tex] b = \frac{14}{sine (23)}*sine (48)
[/tex]
[tex] b = 26.63
[/tex]
Answer:
The values of C, b and c are given by:
109; 26.63cm; 33.88cm
