For a given constant $b > 10,$ there are two possible triangles $ABC$ satisfying $AB = 10,$ $AC = b,$ and $\sin B = \frac{3}{5}.$  Find the positive difference between the lengths of side $\overline{BC}$ in these two triangles.
Question:
For a given constant $b > 10,$ there are two possible triangles $ABC$ satisfying $AB = 10,$ $AC = b,$ and $\sin B = \frac{3}{5}.$  Find the positive difference between the lengths of side $\overline{BC}$ in these two triangles.
Answer:
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For a given constant $b > 10,$ there are two possible triangles $ABC$ satisfying $AB = 10,$ $AC = b,$ and $\sin B = \frac{3}{5}.$  Find the positive difference between the lengths of side $\overline{BC}$ in these two triangles.
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