\(In $\triangle ABC$, we have $\angle BAC = 60^\circ$ and $\angle ABC = 45^\circ$. The bisector of $\angle A$ intersects $\overline{BC}$ at point $T$, and $AT = 24$. What is the area of $\triangle ABC$? [asy] pair A,B,C,T,X,Y; A = (0,0); C = rotate(60)*(1,0); B = (0.5+sqrt(3)/2,0); T = intersectionpoint (C--B, A -- (rotate(30)*(5,0))); draw(T--A--C--B--A); label("$A$",A,SW); label("$B$",B,SW); label("$C$",C,N); label("$T$",T,NE); [/asy]\)
