Solving Isosceles Triangle with all angles and perimeter

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I know that you need at least one side to solve an isosceles triangle given the angles but is it possible to determine the side lengths of an isosceles triangle given the perimeter and all angles?

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$${a \over \sin A} = {b \over \sin B} \Rightarrow {a} = {b * \sin A \over \sin B}$$

$$ 2b + a = P \Rightarrow 2b + {b * \sin A \over \sin B} = P$$