A trivial triangle makeover

Geometry Level 4

A $$\triangle ABC$$ is isosceles ($$AB = AC$$) with $$\angle BAC = 120°$$. What would be $$\angle A_{1}BC$$ (in degrees) if distance between point $$A_{1}$$ and segment $$BC$$ is $$h + a(1 + \sqrt{3})$$.

Notes:

$$h$$ - distance between segment $$BC$$ and point $$A$$

$$a$$ - length of $$AB$$ (or $$AC$$)

$$\triangle A_{1}BC$$ is also isosceles ($$A_{1}B = A_{1}C$$)

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