You can use the law of Cosines to solve an SSS triangle.
[tex] cos A = \frac{b^2 + c^2 - a^2}{2bc}[/tex]
a = 13
b = 21
c = 29
Lets find A first:
[tex] cos A = \frac{b^2 + c^2 - a^2}{2bc}[/tex]
[tex] cos A = \frac{21^2 + 29^2 - 13^2}{2(21)(29)}[/tex]
[tex] cos A = \frac{441+ 841 - 169}{1218}[/tex]
[tex] cos A = \frac{1113}{1218}[/tex]
[tex] cos A = \frac{53}{58}[/tex]
[tex]A = cos^{-1}(\frac{53}{58}) = 23.96509[/tex]
Now lets find B
[tex] cos B = \frac{a^2 + c^2 - b^2}{2ac}[/tex]
[tex] cos B = \frac{13^2 + 29^2 - 21^2}{2(13)(29)}[/tex]
[tex] cos B = \frac{169 + 841 - 441}{754}[/tex]
[tex] cos B = \frac{569}{754}[/tex]
[tex] B = cos^{-1}(\frac{569}{754}) = 41.0059[/tex]
Since we know A and B we can use
C = 180 - A - B to find C
C = 180 - A - B
C = 180 - 23.96509 - 41.0059
C = 115.0291
A = 23.9650
B = 41.0059
C = 115.0291
Round to nearest tenths.
A = 24.0
B = 41.0
C = 115.0
