{"id":26069,"date":"2023-05-25T18:10:55","date_gmt":"2023-05-25T17:10:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26069"},"modified":"2023-05-25T19:16:03","modified_gmt":"2023-05-25T18:16:03","slug":"um-triangulo-abc-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26069","title":{"rendered":"Um tri\u00e2ngulo [ABC]"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26069' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26069' class='GTTabs_curr'><a  id=\"26069_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_26069' ><a  id=\"26069_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_26069'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Do tri\u00e2ngulo [ABC], sabe-se que \u00e9 ret\u00e2ngulo em A e que a amplitude \u03b1 \u00e9 o dobro da amplitude \u03b2.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26071\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26071\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\" data-orig-size=\"247,206\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag205-17\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\" class=\"aligncenter wp-image-26071\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\" alt=\"\" width=\"200\" height=\"167\" \/><\/a><\/p>\n<p>Calcula as amplitudes \u03b1 e \u03b2.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26069' onClick='GTTabs_show(1,26069)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26069'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Do tri\u00e2ngulo [ABC], sabe-se que \u00e9 ret\u00e2ngulo em A e que a amplitude \u03b1 \u00e9 o dobro da amplitude \u03b2.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26071\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26071\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\" data-orig-size=\"247,206\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&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;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"8_Pag205-17\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\" class=\"aligncenter wp-image-26071\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17.png\" alt=\"\" width=\"200\" height=\"167\" \/><\/a><\/p>\n<blockquote>\n<p>Calcula as amplitudes \u03b1 e \u03b2.<\/p>\n<\/blockquote>\n<p><br \/>Equacionando o problema e resolvendo o sistema de equa\u00e7\u00f5es, vem: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{\\alpha + \\beta = 90^\\circ }\\\\{\\alpha = 2\\beta }\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{2\\beta + \\beta = 90^\\circ }\\\\{\\alpha = 2\\beta }\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{\\beta = 30^\\circ }\\\\{\\alpha = 60^\\circ }\\end{array}} \\right.}\\end{array}\\]<\/p>\n<p>Portanto, \\({\\alpha = 60^\\circ }\\) e \\({\\beta = 30^\\circ }\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26069' onClick='GTTabs_show(0,26069)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Do tri\u00e2ngulo [ABC], sabe-se que \u00e9 ret\u00e2ngulo em A e que a amplitude \u03b1 \u00e9 o dobro da amplitude \u03b2. Calcula as amplitudes \u03b1 e \u03b2. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":26072,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,714],"tags":[424,345,239],"series":[],"class_list":["post-26069","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-equacoes-literais-e-sistemas","tag-8-o-ano","tag-funcao-afim","tag-sistema-de-equacoes"],"views":59,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-17_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26069","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=26069"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26069\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26072"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26069"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26069"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26069"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26069"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}