{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","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":"2026-04-06T00:00:00.000Z","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":45180,"title":"All flights lead to Idaho Falls","description":"Using spherical trigonometry and great circle paths, determine the distance (in kilometers) and the initial flight heading (from true North) to the Idaho Falls airport (43d30m49.4sN, 112d4m14.7sW) from an initial starting latitude and longitude in the World. Use an Earth radius of 6371.0088 kilometers. Round to the nearest tenth of a degree or nearest kilometer.\r\n\r\n  lat='19d26m10.6sN';%input\r\n  long='99d4m20.2sW';%input\r\n  distance = 2939;%output\r\n  heading = 338.5;%output\r\n","description_html":"\u003cp\u003eUsing spherical trigonometry and great circle paths, determine the distance (in kilometers) and the initial flight heading (from true North) to the Idaho Falls airport (43d30m49.4sN, 112d4m14.7sW) from an initial starting latitude and longitude in the World. Use an Earth radius of 6371.0088 kilometers. Round to the nearest tenth of a degree or nearest kilometer.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003elat='19d26m10.6sN';%input\r\nlong='99d4m20.2sW';%input\r\ndistance = 2939;%output\r\nheading = 338.5;%output\r\n\u003c/pre\u003e","function_template":"function [distance,heading] = IdahoFalls(lat,long)\r\n  distance = 1;\r\n  heading = 1;\r\nend","test_suite":"%%\r\nlat='19d26m10.6sN';\r\nlong='99d4m20.2sW';\r\ny_correct = [2939,338.5];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='22d18m32.1sN';\r\nlong='113d54m52.8sE';\r\ny_correct = [11322,32.2];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='33d56m46sS';\r\nlong='151d10m38sE';\r\ny_correct = [13019,54.0];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='40d38m24.3sN';\r\nlong='73d46m42.9sW';\r\ny_correct = [3149,288.7];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='55d58m20.7sN';\r\nlong='37d24m47.1sE';\r\ny_correct = [8588,337.8];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='46d36m24sN';\r\nlong='111d59m0.1sW';\r\ny_correct = [344,181.2];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-10-20T04:01:11.000Z","updated_at":"2025-10-11T15:29:11.000Z","published_at":"2019-10-20T04:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing spherical trigonometry and great circle paths, determine the distance (in kilometers) and the initial flight heading (from true North) to the Idaho Falls airport (43d30m49.4sN, 112d4m14.7sW) from an initial starting latitude and longitude in the World. Use an Earth radius of 6371.0088 kilometers. Round to the nearest tenth of a degree or nearest kilometer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[lat='19d26m10.6sN';%input\\nlong='99d4m20.2sW';%input\\ndistance = 2939;%output\\nheading = 338.5;%output]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":45180,"title":"All flights lead to Idaho Falls","description":"Using spherical trigonometry and great circle paths, determine the distance (in kilometers) and the initial flight heading (from true North) to the Idaho Falls airport (43d30m49.4sN, 112d4m14.7sW) from an initial starting latitude and longitude in the World. Use an Earth radius of 6371.0088 kilometers. Round to the nearest tenth of a degree or nearest kilometer.\r\n\r\n  lat='19d26m10.6sN';%input\r\n  long='99d4m20.2sW';%input\r\n  distance = 2939;%output\r\n  heading = 338.5;%output\r\n","description_html":"\u003cp\u003eUsing spherical trigonometry and great circle paths, determine the distance (in kilometers) and the initial flight heading (from true North) to the Idaho Falls airport (43d30m49.4sN, 112d4m14.7sW) from an initial starting latitude and longitude in the World. Use an Earth radius of 6371.0088 kilometers. Round to the nearest tenth of a degree or nearest kilometer.\u003c/p\u003e\u003cpre class=\"language-matlab\"\u003elat='19d26m10.6sN';%input\r\nlong='99d4m20.2sW';%input\r\ndistance = 2939;%output\r\nheading = 338.5;%output\r\n\u003c/pre\u003e","function_template":"function [distance,heading] = IdahoFalls(lat,long)\r\n  distance = 1;\r\n  heading = 1;\r\nend","test_suite":"%%\r\nlat='19d26m10.6sN';\r\nlong='99d4m20.2sW';\r\ny_correct = [2939,338.5];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='22d18m32.1sN';\r\nlong='113d54m52.8sE';\r\ny_correct = [11322,32.2];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='33d56m46sS';\r\nlong='151d10m38sE';\r\ny_correct = [13019,54.0];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='40d38m24.3sN';\r\nlong='73d46m42.9sW';\r\ny_correct = [3149,288.7];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='55d58m20.7sN';\r\nlong='37d24m47.1sE';\r\ny_correct = [8588,337.8];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n%%\r\nlat='46d36m24sN';\r\nlong='111d59m0.1sW';\r\ny_correct = [344,181.2];\r\n[a,b]=IdahoFalls(lat,long);\r\nassert(isequal([a,b],y_correct))\r\n","published":true,"deleted":false,"likes_count":0,"comments_count":0,"created_by":145982,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":5,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2019-10-20T04:01:11.000Z","updated_at":"2025-10-11T15:29:11.000Z","published_at":"2019-10-20T04:18:37.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\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\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eUsing spherical trigonometry and great circle paths, determine the distance (in kilometers) and the initial flight heading (from true North) to the Idaho Falls airport (43d30m49.4sN, 112d4m14.7sW) from an initial starting latitude and longitude in the World. Use an Earth radius of 6371.0088 kilometers. Round to the nearest tenth of a degree or nearest kilometer.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"code\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003e\u003c![CDATA[lat='19d26m10.6sN';%input\\nlong='99d4m20.2sW';%input\\ndistance = 2939;%output\\nheading = 338.5;%output]]\u003e\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"term":"tag:\"spherical 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