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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 a1a2 in that order?

 Oct 3, 2024
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By the Law of Cosines, a_1 = 6 - 2*sqrt(2) and a_2 = 6 + 2*sqrt(2).

 Oct 4, 2024

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