A Truncated Triangle

The
top of an isosceles triangle has been cut off, with the cutting line in
parallel with the triangle's base. The length of the cut is 5 cm. The
length of the remainder's sloping side is 10 cm. The total area of the
two parts is exactly 80 cm². To five decimal places of accuracy, what is the triangle's base angle? |

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Last Updated: January 14th, 2010.