Determine the interior angles of triangle ABC for A(5,1), B(4, -7), and C (-1,-8)

Firs of all we calculate the distances of the sides AB, BC, CA. Then AB = √(((4-5)^2)+((-7-1)^2)) = 8.06; the distance BC will be calculated as BC=√(((-1-4)^2) + ((-8+7)^2)) = 5.1 and side CA will be √(((5+1)^2)+((-8-1)^2))= 10.81. Using first the cosin theorem and then the sin theorem the angles are obtained.