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In the figure, angles $ABC$ and $AST$ are right angles. If $AC = 35$, $AT = 11$, and $BT = 9$, then what is $AS$? [asy] pair A,B,C,D,EE; B = (0,0); A = (1,0); C = (0,0.7); EE = (0.4,0); D = foot(EE,A,C); draw(D--EE--A--C--B--E); draw(rightanglemark(A,B,C,1.5)); draw(rightanglemark(EE,D,A,1.5)); label("$B$",B,SW); label("$A$",A,SE); label("$C$",C,NW); label("$S$",D,NE); label("$T$",EE,S); [/asy]

 Jul 13, 2022
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By similar triangles, AS = 20/3.

 Jul 13, 2022

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