A \( 50-60-70\) triangle is a triangle in which two of the side lengths, measured in millimetres, are different numbers taken from the set \( \{ 50,60,70 \} \), with the remaining number being one of the angles in the triangle, measured in degrees.
Of all \(50-60-70\) triangles, one has a smaller perimeter than the rest.
If this perimeter is \(P\)mm, what is \(P\) (to 4 sig.figs.)?
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