Question 86015
a=12, b=10 and c=8

Use the cosine rule
{{{cos(A) = (b^2 + c^2 - a^2)/(2bc)}}}
{{{cos(A) = (10^2 + 8^2 - 12^2)/(2x10x8)}}}
{{{cos(A) = 20/160}}}
{{{cos(A) = 1/8}}}
{{{A = arccos(1/8) = 82.82^o}}}


Similarly, 
{{{cos(B) = (c^2 + a^2 - b^2)/(2ca)}}}
{{{cos(B) = (8^2 + 12^2 - 10^2)/(2x8x12)}}}
{{{cos(B) = 9/16}}}
{{{B = arccos(9/16) = 55.77^o}}}


Now we have to find angle C
{{{C = 180^o - A - B}}}
{{{C = 180^o - 82.82^o - 55.77^o = 41.41^o}}}