{"status": "success", "data": {"description_md": "A triangle has area $30$, one side of length $10$, and the median to that side of length $9$.  Let $\\theta$ be the acute angle formed by that side and the median.  What is $\\sin{\\theta}$?\n\n$\\textbf{(A)}\\ \\frac{3}{10}\\qquad\\textbf{(B)}\\ \\frac{1}{3}\\qquad\\textbf{(C)}\\ \\frac{9}{20}\\qquad\\textbf{(D)}\\ \\frac{2}{3}\\qquad\\textbf{(E)}\\ \\frac{9}{10}$\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 triangle has area  <span class=\"katex--inline\">30</span> , one side of length  <span class=\"katex--inline\">10</span> , and the median to that side of length  <span class=\"katex--inline\">9</span> .  Let  <span class=\"katex--inline\">\\theta</span>  be the acute angle formed by that side and the median.  What is  <span class=\"katex--inline\">\\sin{\\theta}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{3}{10}\\qquad\\textbf{(B)}\\ \\frac{1}{3}\\qquad\\textbf{(C)}\\ \\frac{9}{20}\\qquad\\textbf{(D)}\\ \\frac{2}{3}\\qquad\\textbf{(E)}\\ \\frac{9}{10}</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": 2, "problem_name": "2012 AMC 12A Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12A_p11", "prev": "/problem/12_amc12A_p09"}}