{"id":2761,"date":"2025-08-13T18:36:15","date_gmt":"2025-08-13T18:36:15","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2761"},"modified":"2025-10-20T15:47:01","modified_gmt":"2025-10-20T15:47:01","slug":"triangle-trigonometrybackground-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/triangle-trigonometrybackground-youll-need-3\/","title":{"raw":"Triangle Trigonometry: Background You'll Need 3","rendered":"Triangle Trigonometry: Background You&#8217;ll Need 3"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Use the triangle angle sum property to find missing angles<\/span><\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\r\n<h3>triangle angle sum theorem<\/h3>\r\n<p data-start=\"2781\" data-end=\"2865\">The sum of the interior angles of a triangle is always [latex]180^\\circ[\/latex]:<\/p>\r\n<p data-start=\"2867\" data-end=\"2905\">[latex]\r\nA + B + C = 180^\\circ\r\n[\/latex]<\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<p data-start=\"3038\" data-end=\"3141\">Find the missing angle in a triangle where [latex]A = 35^\\circ[\/latex] and [latex]B = 75^\\circ[\/latex].<\/p>\r\n<p data-start=\"3143\" data-end=\"3310\">[reveal-answer q=\"863934\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"863934\"][latex] \\begin{align} A + B + C &amp;= 180^\\circ \\\\ 35^\\circ + 75^\\circ + C &amp;= 180^\\circ \\\\ 110^\\circ + C &amp;= 180^\\circ \\\\ C &amp;= 70^\\circ \\end{align} [\/latex][\/hidden-answer]<\/p>\r\n<p data-start=\"3312\" data-end=\"3347\"><\/p>\r\n\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">Find the missing angle in a right triangle if [latex]A = 28^\\circ[\/latex].[reveal-answer q=\"935381\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"935381\"]\r\n\r\nBecause one angle is [latex]90^\\circ[\/latex], [latex] A + B = 90^\\circ [\/latex]\r\n\r\n[latex] \\begin{align} 28^\\circ + B &amp;= 90^\\circ \\\\ B &amp;= 62^\\circ \\end{align} [\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313832[\/ohm_question]<\/section><section class=\"textbox proTip\" aria-label=\"Pro Tip\">Right triangles are especially easy \u2014 the two acute angles always add up to [latex]90^\\circ[\/latex].<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Use the triangle angle sum property to find missing angles<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox keyTakeaway\" aria-label=\"Key Takeaway\">\n<h3>triangle angle sum theorem<\/h3>\n<p data-start=\"2781\" data-end=\"2865\">The sum of the interior angles of a triangle is always [latex]180^\\circ[\/latex]:<\/p>\n<p data-start=\"2867\" data-end=\"2905\">[latex]A + B + C = 180^\\circ[\/latex]<\/p>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<p data-start=\"3038\" data-end=\"3141\">Find the missing angle in a triangle where [latex]A = 35^\\circ[\/latex] and [latex]B = 75^\\circ[\/latex].<\/p>\n<p data-start=\"3143\" data-end=\"3310\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q863934\">Show Solution<\/button><\/p>\n<div id=\"q863934\" class=\"hidden-answer\" style=\"display: none\">[latex]\\begin{align} A + B + C &= 180^\\circ \\\\ 35^\\circ + 75^\\circ + C &= 180^\\circ \\\\ 110^\\circ + C &= 180^\\circ \\\\ C &= 70^\\circ \\end{align}[\/latex]<\/div>\n<\/div>\n<p data-start=\"3312\" data-end=\"3347\">\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">Find the missing angle in a right triangle if [latex]A = 28^\\circ[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q935381\">Show Solution<\/button><\/p>\n<div id=\"q935381\" class=\"hidden-answer\" style=\"display: none\">\n<p>Because one angle is [latex]90^\\circ[\/latex], [latex]A + B = 90^\\circ[\/latex]<\/p>\n<p>[latex]\\begin{align} 28^\\circ + B &= 90^\\circ \\\\ B &= 62^\\circ \\end{align}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313832\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313832&theme=lumen&iframe_resize_id=ohm313832&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">Right triangles are especially easy \u2014 the two acute angles always add up to [latex]90^\\circ[\/latex].<\/section>\n","protected":false},"author":67,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":221,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2761"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":7,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2761\/revisions"}],"predecessor-version":[{"id":4756,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2761\/revisions\/4756"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/221"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2761\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2761"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2761"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2761"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2761"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}