{"status": "success", "data": {"description_md": "In tetrahedron $ABCD$, edge $AB$ has length 3 cm. The area of face $ABC$ is 15 $\\text{cm}^2$ and the area of face $ABD$ is 12 $\\text{cm}^2$. These two faces meet each other at a $30^\\circ$ angle. Find the volume of the tetrahedron in $\\text{cm}^3$.\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>In tetrahedron <span class=\"katex--inline\">ABCD</span>, edge <span class=\"katex--inline\">AB</span> has length 3 cm. The area of face <span class=\"katex--inline\">ABC</span> is 15 <span class=\"katex--inline\">\\text{cm}^2</span> and the area of face <span class=\"katex--inline\">ABD</span> is 12 <span class=\"katex--inline\">\\text{cm}^2</span>. These two faces meet each other at a <span class=\"katex--inline\">30^\\circ</span> angle. Find the volume of the tetrahedron in <span class=\"katex--inline\">\\text{cm}^3</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": 4, "problem_name": "1984 AIME Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/84_aime_p10", "prev": "/problem/84_aime_p08"}}