{"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":"391522c6-23fb-5bfe-8230-a227263d9e6e","task_key":"precalculus--test--391522c6-23fb-5bfe-8230-a227263d9e6e","task_revision_id":"1","upstream_id":"","short_description":"There are two possible triangles with $AB = 13,$ $BC = 10,$ and $A = 40^\\circ.$…","config":"precalculus","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"There are two possible triangles with $AB = 13,$ $BC = 10,$ and $A = 40^\\\\circ.$  One of them is shown below.  What is the sum of the two possible values of $\\\\angle B,$ in degrees?\\n\\n[asy]\\nunitsize (1 cm);\\n\\npair A, B, C;\\n\\nA = (0,0);\\nB = 5*dir(40);\\nC = (5,0);\\n\\ndraw(A--B--C--cycle);\\n\\nlabel(\\\"$A$\\\", A, SW);\\nlabel(\\\"$B$\\\", B, N);\\nlabel(\\\"$C$\\\", C, SE);\\nlabel(\\\"$13$\\\", (A + B)/2, NW);\\nlabel(\\\"$10$\\\", (B + C)/2, NE);\\nlabel(\\\"$40^\\\\circ$\\\", (1,0.4));\\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":[]}