Question 43785
in triangle ABC, a = 5, b = 9, and c = 6
Use Law of Cosines:
{{{a^2 = b^2 + c^2 - 2bc(cos(A))}}}
{{{(-a^2 + b^2 + c^2)/(2bc) = cos(A)}}}
{{{(-5^2 + 9^2 + 6^2)/(2*9*6) = cos(A)}}}
{{{(-25 + 81 + 36)/(108) = cos(A)}}}
{{{(92)/(108) = cos(A)}}}
{{{cos^(-1)(92/108) = A}}}
{{{32 = A}}}
Use Law of Sines:
{{{Sin(A)/a = Sin(B)/b}}}
{{{Sin(32)/5 = Sin(B)/9}}}
{{{9*Sin(32)/5 = Sin(B)}}}
{{{sin^(-1)(9*Sin(32)/5) = B}}}
{{{73 = B}}}
Use Law of Sum of Interior Angles: {{{180(b - 2)}}} : 180(3 - 2) : 180
180 - (32 + 73) = C
180 - 105 = C
75 = C