CEMC Euclid, 2010

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

A snail's shell is formed from six triangular sections, as shown. Each triangle has interior angles of $30^\circ$ , $60^\circ$ and $90^\circ$ . If $AB$ has a length of 1 cm, what is the length of $AH$ , in cm?

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