{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"5ab7a09e-9d7d-5dbe-b517-825cdb8ee237","task_key":"precalculus--test--5ab7a09e-9d7d-5dbe-b517-825cdb8ee237","task_revision_id":"1","upstream_id":"","short_description":"In the diagram below, we have $AB = 24$ and $\\angle ADB =90^\\circ$. If $\\sin A =…","config":"precalculus","split":"test","body":"{\"level\":\"Level 1\",\"problem\":\"In the diagram below, we have $AB = 24$ and $\\\\angle ADB =90^\\\\circ$.  If $\\\\sin A = \\\\frac23$ and $\\\\sin C = \\\\frac34$, then what is $BC$?\\n\\n\\n[asy]\\npair A,B,C,D;\\nA = (0,0);\\nB = (8*sqrt(5),16);\\nD = (8*sqrt(5),0);\\nC = (8*sqrt(5) + 5.3333*sqrt(7),0);\\ndraw(D--B--A--C--B);\\nlabel(\\\"$A$\\\",A,SW);\\nlabel(\\\"$B$\\\",B,N);\\nlabel(\\\"$C$\\\",C,SE);\\nlabel(\\\"$D$\\\",D,S);\\ndraw(rightanglemark(B,D,A,43));\\n[/asy]\",\"type\":\"Precalculus\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}