Question

Find the degrees of all the sides

Answer 1

You can use the law of Cosines to solve  an SSS triangle.

$cos A = \frac{b^2 + c^2 - a^2}{2bc}$
a = 13
b = 21
c = 29
Lets find A first:
$cos A = \frac{b^2 + c^2 - a^2}{2bc}$
$cos A = \frac{21^2 + 29^2 - 13^2}{2(21)(29)}$
$cos A = \frac{441+ 841 - 169}{1218}$
$cos A = \frac{1113}{1218}$
$cos A = \frac{53}{58}$

$A = cos^{-1}(\frac{53}{58}) = 23.96509$

Now lets find B
$cos B = \frac{a^2 + c^2 - b^2}{2ac}$
$cos B = \frac{13^2 + 29^2 - 21^2}{2(13)(29)}$
$cos B = \frac{169 + 841 - 441}{754}$
$cos B = \frac{569}{754}$

$B = cos^{-1}(\frac{569}{754}) = 41.0059$

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