MathDB
Angle Bisector

Source:

December 6, 2005
geometrytrigonometrytrig identitiesLaw of Sines

Problem Statement

In triangle ABCABC, angles AA and BB measure 60 degrees and 45 degrees, respectively. The bisector of angle AA intersects BC‾\overline{BC} at TT, and AT=24.AT=24. The area of triangle ABCABC can be written in the form a+bc,a+b\sqrt{c}, where aa, bb, and cc are positive integers, and cc is not divisible by the square of any prime. Find a+b+c.a+b+c.
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