{"id":4492,"date":"2023-06-13T04:10:39","date_gmt":"2023-06-13T04:10:39","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=4492"},"modified":"2025-08-26T03:29:44","modified_gmt":"2025-08-26T03:29:44","slug":"triangles-apply-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/triangles-apply-it-1\/","title":{"raw":"Triangles: Apply It 1","rendered":"Triangles: Apply It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Classify triangles based on their angles and side lengths<\/li>\r\n\t<li>Determine the measure of the third angle in a triangle when the measures of two angles are given<\/li>\r\n\t<li>Apply properties of similar triangles to find unknown side lengths<\/li>\r\n\t<li>Use the Pythagorean theorem to calculate unknown side lengths in triangles<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Triangle Troupe: A Physics Adventure at the Circus<\/h2>\r\n<p>You have been recruited to help Luca and Mia, two physics students who are working as interns at a popular circus during the summer break. They have been asked to use their knowledge of triangles to help with various tasks around the circus. Ready to help?<\/p>\r\n<center>\r\n[caption id=\"attachment_6691\" align=\"aligncenter\" width=\"500\"]<img class=\"wp-image-6691\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-300x200.jpg\" alt=\"A circus\" width=\"500\" height=\"333\" \/> Figure 1. Use your knowledge on triangles to help Luca and Mia carry out their tasks[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>Luca and Mia are setting up a large circus tent which has a triangle at its front. The triangle has angles [latex]45\u00b0[\/latex], [latex]45\u00b0[\/latex], and [latex]90\u00b0[\/latex].<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9559[\/ohm2_question]<\/section>\r\n<p>Now that the circus tent is set up the clowns can preform. Luca is helping the clowns get ready for their show. He notices the clown's hat is made of fabric that forms a triangle with sides of equal length. If all three sides of the triangle are each [latex]7[\/latex]cm, which type of triangle does the hat represent?<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9560[\/ohm2_question]<\/section>\r\n<p>While Luca is helping the clowns get ready, Mia is checking on the lights for the show. Mia decides new spotlight pattern is needed. Her new pattern forms a triangle with angles [latex]47\u00b0[\/latex], [latex]102\u00b0[\/latex], and [latex]31\u00b0[\/latex]. What type of triangle is she using for her design?<\/p>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]9561[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Classify triangles based on their angles and side lengths<\/li>\n<li>Determine the measure of the third angle in a triangle when the measures of two angles are given<\/li>\n<li>Apply properties of similar triangles to find unknown side lengths<\/li>\n<li>Use the Pythagorean theorem to calculate unknown side lengths in triangles<\/li>\n<\/ul>\n<\/section>\n<h2>Triangle Troupe: A Physics Adventure at the Circus<\/h2>\n<p>You have been recruited to help Luca and Mia, two physics students who are working as interns at a popular circus during the summer break. They have been asked to use their knowledge of triangles to help with various tasks around the circus. Ready to help?<\/p>\n<div style=\"text-align: center;\">\n<figure id=\"attachment_6691\" aria-describedby=\"caption-attachment-6691\" style=\"width: 500px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-6691\" src=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-300x200.jpg\" alt=\"A circus\" width=\"500\" height=\"333\" srcset=\"https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-300x200.jpg 300w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-1024x681.jpg 1024w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-768x511.jpg 768w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-1536x1022.jpg 1536w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-2048x1363.jpg 2048w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-1200x799.jpg 1200w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-65x43.jpg 65w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-225x150.jpg 225w, https:\/\/content-cdn.one.lumenlearning.com\/wp-content\/uploads\/sites\/18\/2023\/06\/12211519\/pexels-brett-sayles-9708620_50-350x233.jpg 350w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><figcaption id=\"caption-attachment-6691\" class=\"wp-caption-text\">Figure 1. Use your knowledge on triangles to help Luca and Mia carry out their tasks<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Luca and Mia are setting up a large circus tent which has a triangle at its front. The triangle has angles [latex]45\u00b0[\/latex], [latex]45\u00b0[\/latex], and [latex]90\u00b0[\/latex].<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9559\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9559&theme=lumen&iframe_resize_id=ohm9559&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Now that the circus tent is set up the clowns can preform. Luca is helping the clowns get ready for their show. He notices the clown&#8217;s hat is made of fabric that forms a triangle with sides of equal length. If all three sides of the triangle are each [latex]7[\/latex]cm, which type of triangle does the hat represent?<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9560\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9560&theme=lumen&iframe_resize_id=ohm9560&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>While Luca is helping the clowns get ready, Mia is checking on the lights for the show. Mia decides new spotlight pattern is needed. Her new pattern forms a triangle with angles [latex]47\u00b0[\/latex], [latex]102\u00b0[\/latex], and [latex]31\u00b0[\/latex]. What type of triangle is she using for her design?<\/p>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm9561\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=9561&theme=lumen&iframe_resize_id=ohm9561&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":23,"menu_order":15,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Gray Circus Tent during Nighttime\",\"author\":\"Zachary DeBottis\",\"organization\":\"Pexels\",\"url\":\"https:\/\/www.pexels.com\/photo\/gray-circus-tent-during-nighttime-2002338\/\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":71,"module-header":"apply_it","content_attributions":[{"type":"copyrighted_video","description":"Gray Circus Tent during Nighttime","author":"Zachary DeBottis","organization":"Pexels","url":"https:\/\/www.pexels.com\/photo\/gray-circus-tent-during-nighttime-2002338\/","project":"","license":"arr","license_terms":""}],"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\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4492"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/23"}],"version-history":[{"count":12,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4492\/revisions"}],"predecessor-version":[{"id":15647,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4492\/revisions\/15647"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/71"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/4492\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=4492"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=4492"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=4492"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=4492"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}