{"status": "success", "data": {"description_md": "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 $AC^2$?<br><center><img class=\"problem-image\" alt='[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]' class=\"latexcenter\" height=\"182\" src=\"https://latex.artofproblemsolving.com/4/2/b/42be593c3f7699bcb004014182d54b6832e3e173.png\" width=\"255\"/></center>\n\n$\\textbf{(A)}\\ [400,500] \\qquad \\textbf{(B)}\\ [500,600] \\qquad \\textbf{(C)}\\ [600,700] \\qquad \\textbf{(D)}\\ [700,800] \\qquad \\textbf{(E)}\\ [800,900]$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>A ship sails  <span class=\"katex--inline\">10</span>  miles in a straight line from  <span class=\"katex--inline\">A</span>  to  <span class=\"katex--inline\">B</span> , turns through an angle between  <span class=\"katex--inline\">45^{\\circ}</span>  and  <span class=\"katex--inline\">60^{\\circ}</span> , and then sails another  <span class=\"katex--inline\">20</span>  miles to  <span class=\"katex--inline\">C</span> . Let  <span class=\"katex--inline\">AC</span>  be measured in miles. Which of the following intervals contains  <span class=\"katex--inline\">AC^2</span> ?<br/><center><img class=\"latexcenter\" alt=\"[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(&#34;4 4&#34;));  dot(A); dot(B); dot(C); label(&#34;$10$&#34;,midpoint(A--B),S); label(&#34;$20$&#34;,midpoint(B--C),SE); label(&#34;$A$&#34;,A,SW); label(&#34;$B$&#34;,B,SE); label(&#34;$C$&#34;,C,NE); [/asy]\" height=\"182\" src=\"https://latex.artofproblemsolving.com/4/2/b/42be593c3f7699bcb004014182d54b6832e3e173.png\" width=\"255\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ [400,500] \\qquad \\textbf{(B)}\\ [500,600] \\qquad \\textbf{(C)}\\ [600,700] \\qquad \\textbf{(D)}\\ [700,800] \\qquad \\textbf{(E)}\\ [800,900]</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2009 AMC 12A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/09_amc12A_p14", "prev": "/problem/09_amc12A_p12"}}