{"id":4155,"date":"2010-10-18T15:29:53","date_gmt":"2010-10-18T14:29:53","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=4155"},"modified":"2022-01-18T23:35:18","modified_gmt":"2022-01-18T23:35:18","slug":"comprimento-dos-lados-do-triangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=4155","title":{"rendered":"Comprimento dos lados do tri\u00e2ngulo"},"content":{"rendered":"<p style=\"text-align: left;\"><ul id='GTTabs_ul_4155' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_4155' class='GTTabs_curr'><a  id=\"4155_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_4155' ><a  id=\"4155_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_4155'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Coloca por ordem decrescente as medidas dos comprimentos dos lados do tri\u00e2ngulo [XYZ].<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4158\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4158\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9.jpg\" data-orig-size=\"441,311\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tri\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9.jpg\" class=\"aligncenter wp-image-4158\" title=\"Tri\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-300x211.jpg\" alt=\"\" width=\"300\" height=\"212\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-300x211.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-150x105.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-400x282.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9.jpg 441w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_4155' onClick='GTTabs_show(1,4155)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_4155'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"4158\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=4158\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9.jpg\" data-orig-size=\"441,311\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Tri\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9.jpg\" class=\"alignright wp-image-4158\" title=\"Tri\u00e2ngulo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-300x211.jpg\" alt=\"\" width=\"300\" height=\"212\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-300x211.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-150x105.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9-400x282.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/pag95-9.jpg 441w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Come\u00e7ando por determinar a amplitude dos \u00e2ngulos internos do tri\u00e2ngulo, temos (Porqu\u00ea?): \\[\\begin{array}{*{35}{l}}<br \/>\nX\\widehat{Y}Z &amp; = &amp; 180{}^\\text{o}-110{}^\\text{o}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 70{}^\\text{o}\u00a0 \\\\<br \/>\n\\end{array}\\]<br \/>\ne (Porqu\u00ea?)\u00a0\\[\\begin{array}{*{35}{l}}<br \/>\nX\\widehat{Z}Y &amp; = &amp; 180{}^\\text{o}-(Y\\widehat{X}Z+X\\widehat{Y}Z)\u00a0 \\\\<br \/>\n{} &amp; = &amp; 180{}^\\text{o}-(35{}^\\text{o}+70{}^\\text{o})\u00a0 \\\\<br \/>\n{} &amp; = &amp; 75{}^\\text{o}\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>Dado que, num tri\u00e2ngulo, ao maior \u00e2ngulo se op\u00f5e o maior lado e ao menor \u00e2ngulo se op\u00f5e o menor lado, ser\u00e1: \\[\\overline{XY}&gt;\\overline{XZ}&gt;\\overline{YZ}\\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_4155' onClick='GTTabs_show(0,4155)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Coloca por ordem decrescente as medidas dos comprimentos dos lados do tri\u00e2ngulo [XYZ]. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20622,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,102],"tags":[424,105,67,106],"series":[],"class_list":["post-4155","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-do-espaco-ao-plano","tag-8-o-ano","tag-angulos","tag-geometria","tag-triangulos"],"views":2573,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/10\/7V2Pag095-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4155"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/4155\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20622"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4155"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4155"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=4155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}