Find the angle C of the triangle ABC, if BC = a, AC = b, and its area is S solve this problem

Find the angle C of the triangle ABC, if BC = a, AC = b, and its area is S solve this problem if 1) a = 7 b = 8 S = 14 2) a = 12, b = 5 √ 3, S = 45

Let’s apply the area formula: S = a * b * sin (<C), whence sin C = S / a * b. Substituting the values into the formula, we get the angle value <C:

1) sin С = 14 / (7 * 8) = 2/8 = 0.25. <C = arc sin (0.25).

2) sin С = 45 / (12 * 5√3) = 9 / 12√3 = √3 / 4. <C = arc sin (√3 / 4).