{"id":26110,"date":"2023-05-26T17:26:19","date_gmt":"2023-05-26T16:26:19","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=26110"},"modified":"2023-05-26T17:38:32","modified_gmt":"2023-05-26T16:38:32","slug":"um-problema-de-angulos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=26110","title":{"rendered":"Um problema de \u00e2ngulos"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_26110' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_26110' class='GTTabs_curr'><a  id=\"26110_0\" onMouseOver=\"GTTabsShowLinks('Eunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Eunciado<\/a><\/li>\n<li id='GTTabs_li_1_26110' ><a  id=\"26110_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_26110'>\n<span class='GTTabs_titles'><b>Eunciado<\/b><\/span><\/p>\n<p>Sabendo que a amplitude do \u00e2ngulo \u03b1 \u00e9 \\(\\frac{1}{4}\\) da amplitude do \u00e2ngulo \u03b2, qual \u00e9 a medida da amplitude de cada um destes \u00e2ngulos?<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26111\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26111\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\" data-orig-size=\"250,94\" 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_Pag205-20\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\" class=\"aligncenter wp-image-26111\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\" alt=\"\" width=\"250\" height=\"94\" \/><\/a><\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_26110' onClick='GTTabs_show(1,26110)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_26110'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Sabendo que a amplitude do \u00e2ngulo \u03b1 \u00e9 \\(\\frac{1}{4}\\) da amplitude do \u00e2ngulo \u03b2, qual \u00e9 a medida da amplitude de cada um destes \u00e2ngulos?<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"26111\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=26111\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\" data-orig-size=\"250,94\" 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_Pag205-20\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\" class=\"aligncenter wp-image-26111\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20.png\" alt=\"\" width=\"250\" height=\"94\" \/><\/a><\/p>\n<p>Equacionando o problema e resolvendo o sistema de equa\u00e7\u00f5es, vem: \\[\\begin{array}{*{20}{l}}{\\left\\{ {\\begin{array}{*{20}{l}}{\\alpha + \\beta = 180^\\circ }\\\\{\\alpha = \\frac{1}{4}\\beta }\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{\\frac{1}{4}\\beta + \\beta = 180^\\circ }\\\\{\\alpha = \\frac{1}{4}\\beta }\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{\\frac{5}{4}\\beta = 180^\\circ }\\\\{\\alpha = \\frac{1}{4}\\beta }\\end{array}} \\right.}&amp; \\Leftrightarrow \\\\{}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{\\beta = \\frac{4}{5} \\times 180^\\circ }\\\\{\\alpha = \\frac{1}{4}\\beta }\\end{array}} \\right.}&amp; \\Leftrightarrow &amp;{\\left\\{ {\\begin{array}{*{20}{l}}{\\beta = 144^\\circ }\\\\{\\alpha = 36^\\circ }\\end{array}} \\right.}&amp;{}\\end{array}\\]<\/p>\n<p>Portanto, \\({\\alpha = 36^\\circ }\\) e \\({\\beta = 144^\\circ }\\).<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_26110' onClick='GTTabs_show(0,26110)'>&lt;&lt; Eunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Eunciado Resolu\u00e7\u00e3o Eunciado Sabendo que a amplitude do \u00e2ngulo \u03b1 \u00e9 \\(\\frac{1}{4}\\) da amplitude do \u00e2ngulo \u03b2, qual \u00e9 a medida da amplitude de cada um destes \u00e2ngulos? Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Eunciado<\/p>\n","protected":false},"author":1,"featured_media":26112,"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-26110","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":67,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2023\/05\/8_Pag205-20_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26110","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=26110"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/26110\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/26112"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26110"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=26110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}