Case I:
Let x be the side opposite the angle
By cosine rule, x^{2} = 8^{2} + 9^{2} – 2*8*9*cos 60
x^{2} = 145 – 72 = 73
or x =
Case II:
Let 9 cm be the side opposite the angle
By cosine rule, 9^{2} = 8^{2} + x^{2} – 2*8*x*cos 60
17 = x^{2} - 8x
x^{2} - 8x - 17 = 0
or x = (8 +- ) / 2
= 4 +-
Only 4 +
Case III:
Let 8 cm be the side opposite the angle
By cosine rule, 8^{2} = 9^{2} + x^{2} – 2*9*x*cos 60
-17 = x^{2} - 9x
x^{2} - 9x + 17 = 0
or x = (9 +- ) / 2
= 4.5 +- ()/2
=4.5 +-
Correct Answer: (D). Only II, III and IV