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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?

 

 May 14, 2022
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By similar triangles,

\(\dfrac{AB}{AC} = \dfrac{AS}{AT}\\ \dfrac{AT + BT}{AC} = \dfrac{AS}{AT}\\ AS = \dfrac{AT(AT + BT)}{AC} = \dfrac{11(11 + 9)}{35} = \boxed{\dfrac{44}7}\)

 May 14, 2022

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