There are two triangles satisfying ∠BCA=60∘,AB=9 and AC=10 shown below:The possible values of BC are a1 and a2 as shown in the picture with a1<a2. Then what are a1, a2 in that order?
By the Law of Cosines, a_1 = 6 - 2*sqrt(2) and a_2 = 6 + 2*sqrt(2).