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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