Using the Law of Cosines, the values of a, b, and c are approximately 64.62, 52.00, and 56.57, respectively.
The Law of Cosines states that for any triangle with sides of length a, b, and c and angles opposite those sides of length A, B, and C, respectively, the following equation holds:
a² = b² + c² - 2bc*cosA
b² = a² + c² - 2ac*cosB
c² = a² + b² - 2ab*cosC
Angle A = 120°
Angle B = 52°
Angle C = 34°
Substituting the values given in the image, we have:
a = √(52² + 34² - 25234*cos120°) ≈ 64.62
b = √(64.62² + 34² - 264.6234*cos52°) ≈ 52.00
c = √(64.62² + 52² - 264.6252*cos34°) ≈ 56.57
Thus, we can conclude that the values of a, b, and c are approximately 64.62, 52.00, and 56.57, respectively