{"status": "success", "data": {"description_md": "Faces $ABC$ and $BCD$ of tetrahedron $ABCD$ meet at an angle of $30^\\circ$. The area of face $ABC$ is $120$, the area of face $BCD$ is $80$, and $BC=10$. Find the volume of the tetrahedron.\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>Faces <span class=\"katex--inline\">ABC</span> and <span class=\"katex--inline\">BCD</span> of tetrahedron <span class=\"katex--inline\">ABCD</span> meet at an angle of <span class=\"katex--inline\">30^\\circ</span>. The area of face <span class=\"katex--inline\">ABC</span> is <span class=\"katex--inline\">120</span>, the area of face <span class=\"katex--inline\">BCD</span> is <span class=\"katex--inline\">80</span>, and <span class=\"katex--inline\">BC=10</span>. Find the volume of the tetrahedron.</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": "1992 AIME Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/92_aime_p08", "prev": "/problem/92_aime_p06"}}