{"status": "success", "data": {"description_md": "Given that $\\sum_{k=1}^{35}\\sin 5k=\\tan \\frac mn,$ where angles are measured in degrees, and $m$ and $n$ are relatively prime positive integers that satisfy $\\frac mn<90,$ find $m+n.$\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>Given that <span class=\"katex--inline\">\\sum_{k=1}^{35}\\sin 5k=\\tan \\frac mn,</span> where angles are measured in degrees, and <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers that satisfy <span class=\"katex--inline\">\\frac mn&lt;90,</span> find <span class=\"katex--inline\">m+n.</span></p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 5, "problem_name": "1999 AIME Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/99_aime_p12", "prev": "/problem/99_aime_p10"}}