An isosceles triangle has two equal sides of 10 cm enclosing an angle of 120°. Its third side measures:

The altitude from the apex bisects the 120° angle, so half the base is 10·sin60° and the base is $2\times 10$ × (√3/2) = 10√3 ≈ 17.32 cm. The cosine rule agrees: $100+100-2(100)(-1/2)=300$. Taking cos120° as +1/2 collapses the answer to 10 cm, which is impossible — the side opposite an obtuse angle must be the longest.