Problem

2009 AMC 12A Problem 13

A ship sails 10 miles in a straight line from A to B, turns through an angle between 45^{\circ} and 60^{\circ}, and then sails another 20 miles to C. Let AC be measured in miles. Which of the following intervals contains AC^2? [asy] unitsize(2mm); defaultpen(linewidth(.8pt)+fontsize(10pt)); dotfactor=4; pair B=(0,0), A=(-10,0), C=20*dir(50); draw(A--B--C); draw(A--C,linetype("4 4")); dot(A); dot(B); dot(C); label("$10$",midpoint(A--B),S); label("$20$",midpoint(B--C),SE); label("$A$",A,SW); label("$B$",B,SE); label("$C$",C,NE); [/asy]

\textbf{(A)}\ [400,500] \qquad \textbf{(B)}\ [500,600] \qquad \textbf{(C)}\ [600,700] \qquad \textbf{(D)}\ [700,800] \qquad \textbf{(E)}\ [800,900]

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


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Category: AMC 12A
Points: 3
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