2001 AIME I Problem 4

In triangle ABC, angles A and B measure 60 degrees and 45 degrees, respectively. The bisector of angle A intersects \overline{BC} at T, and AT=24. The area of triangle ABC can be written in the form a+b\sqrt{c}, where a, b, and c are positive integers, and c is not divisible by the square of any prime. Find a+b+c.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.