{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-06-05T00:10:21.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-06-05T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":144,"title":"Angle of triangle","description":"For three unknown points a b c, given three sides ab bc ca, find three angles abc bca cab in radians.\r\nYour function should be accurate to four digits and return before 1000 microseconds on this machine.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 317.5px 8px; transform-origin: 317.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor three unknown points a b c, given three sides ab bc ca, find three angles abc bca cab in radians.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 319.5px 8px; transform-origin: 319.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function should be accurate to four digits and return before 1000 microseconds on this machine.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [abc,bca,cab] = sides_to_angles(ab,bc,ca)\r\nabc=pi/3;\r\nbca=pi/3;\r\ncab=pi/3;\r\nend","test_suite":"%%\r\ntic; \r\nfor k=1:10^3\r\nab=rand; bc=rand; ca=max(min(rand, ab+bc),abs(ab-bc));\r\n[abc,bca,cab]=sides_to_angles(ab,bc,ca);\r\nend \r\nyour_time=toc/10^3\r\ntest_yours=round([abc,bca,cab]*10^4)/10^4;\r\nabc=acos((ab^2+bc^2-ca^2)/2/ab/bc);\r\nbca=acos((bc^2+ca^2-ab^2)/2/bc/ca);\r\ncab=acos((ca^2+ab^2-bc^2)/2/ca/ab);\r\ntest_correct=round([abc,bca,cab]*10^4)/10^4;\r\nassert(isequal(test_yours,test_correct))\r\nassert(your_time\u003c100e-5)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":143,"test_suite_updated_at":"2022-01-14T17:42:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-28T11:26:01.000Z","updated_at":"2026-03-31T00:06:18.000Z","published_at":"2012-02-05T23:20:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor three unknown points a b c, given three sides ab bc ca, find three angles abc bca cab in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function should be accurate to four digits and return before 1000 microseconds on this machine.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"problem_search":{"problems":[{"id":144,"title":"Angle of triangle","description":"For three unknown points a b c, given three sides ab bc ca, find three angles abc bca cab in radians.\r\nYour function should be accurate to four digits and return before 1000 microseconds on this machine.","description_html":"\u003cdiv style = \"text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; \"\u003e\u003cdiv style=\"block-size: 51px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 25.5px; transform-origin: 407px 25.5px; vertical-align: baseline; \"\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 317.5px 8px; transform-origin: 317.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eFor three unknown points a b c, given three sides ab bc ca, find three angles abc bca cab in radians.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003cdiv style=\"block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; \"\u003e\u003cspan style=\"block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 319.5px 8px; transform-origin: 319.5px 8px; unicode-bidi: normal; \"\u003e\u003cspan style=\"\"\u003eYour function should be accurate to four digits and return before 1000 microseconds on this machine.\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e","function_template":"function [abc,bca,cab] = sides_to_angles(ab,bc,ca)\r\nabc=pi/3;\r\nbca=pi/3;\r\ncab=pi/3;\r\nend","test_suite":"%%\r\ntic; \r\nfor k=1:10^3\r\nab=rand; bc=rand; ca=max(min(rand, ab+bc),abs(ab-bc));\r\n[abc,bca,cab]=sides_to_angles(ab,bc,ca);\r\nend \r\nyour_time=toc/10^3\r\ntest_yours=round([abc,bca,cab]*10^4)/10^4;\r\nabc=acos((ab^2+bc^2-ca^2)/2/ab/bc);\r\nbca=acos((bc^2+ca^2-ab^2)/2/bc/ca);\r\ncab=acos((ca^2+ab^2-bc^2)/2/ca/ab);\r\ntest_correct=round([abc,bca,cab]*10^4)/10^4;\r\nassert(isequal(test_yours,test_correct))\r\nassert(your_time\u003c100e-5)","published":true,"deleted":false,"likes_count":1,"comments_count":2,"created_by":166,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":143,"test_suite_updated_at":"2022-01-14T17:42:43.000Z","rescore_all_solutions":false,"group_id":1,"created_at":"2012-01-28T11:26:01.000Z","updated_at":"2026-03-31T00:06:18.000Z","published_at":"2012-02-05T23:20:43.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eFor three unknown points a b c, given three sides ab bc ca, find three angles abc bca cab in radians.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003cw:jc w:val=\\\"left\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eYour function should be accurate to four digits and return before 1000 microseconds on this machine.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\",\"relationship\":null}],\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"target\":\"/matlab/document.xml\",\"relationshipId\":\"rId1\"}]}"}],"errors":[],"facets":[[],[{"value":"easy","count":1,"selected":false}]],"term":"tag:\"fast angle triangle geometry\"","page":1,"per_page":50,"sort":"map(difficulty_value,0,0,999) asc"}}