{"id":14145,"date":"2018-03-12T21:32:54","date_gmt":"2018-03-12T21:32:54","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14145"},"modified":"2022-01-11T10:52:40","modified_gmt":"2022-01-11T10:52:40","slug":"o-quadrilatero-abcd-esta-dividido-em-dois-triangulos-retangulos","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14145","title":{"rendered":"O quadril\u00e1tero [ABCD] est\u00e1 dividido em dois tri\u00e2ngulos ret\u00e2ngulos"},"content":{"rendered":"<p><ul id='GTTabs_ul_14145' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14145' class='GTTabs_curr'><a  id=\"14145_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14145' ><a  id=\"14145_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_14145'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14146\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14146\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png\" data-orig-size=\"425,245\" 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=\"Quadril\u00e1tero\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png\" class=\"alignright wp-image-14146\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9-300x173.png\" alt=\"\" width=\"360\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9-300x173.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png 425w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>O quadril\u00e1tero [<em>ABCD<\/em>] est\u00e1 dividido em dois tri\u00e2ngulos ret\u00e2ngulos.<\/p>\n<ol>\n<li>Qual \u00e9 a medida da amplitude do \u00e2ngulo <em>BAC<\/em>, arredondada \u00e0s unidades?\u00a0Explica como chegaste \u00e0 tua resposta.<\/li>\n<li>Determina\u00a0\\(\\overline {AD} \\) arredondado \u00e0s d\u00e9cimas.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14145' onClick='GTTabs_show(1,14145)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14145'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14146\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14146\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png\" data-orig-size=\"425,245\" 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=\"Quadril\u00e1tero\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png\" class=\"alignright wp-image-14146\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9-300x173.png\" alt=\"\" width=\"360\" height=\"208\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9-300x173.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9.png 425w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo [<em>ABC<\/em>], temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} B\\widehat AC = \\frac{{\\overline {BC} }}{{\\overline {AC} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} B\\widehat AC = \\frac{{3,6}}{{7,2}}}\\\\{}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} B\\widehat AC = \\frac{1}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{B\\widehat AC = {{{\\mathop{\\rm tg}\\nolimits} }^{ &#8211; 1}}\\left( {\\frac{1}{2}} \\right)}\\\\{}&amp;{}&amp;{B\\widehat AC \\approx 27^\\circ }\\end{array}\\]<br \/>\nPortanto, \\({B\\widehat AC \\approx 27^\\circ }\\).<br \/>\n\u00ad<\/li>\n<li>No tri\u00e2ngulo ret\u00e2ngulo [<em>ACD<\/em>], temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} A\\widehat DC = \\frac{{\\overline {AC} }}{{\\overline {AD} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 59^\\circ = \\frac{{7,2}}{{\\overline {AD} }}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AD} = \\frac{{7,2}}{{{\\mathop{\\rm tg}\\nolimits} 59^\\circ }}}\\\\{}&amp;{}&amp;{\\overline {AD} \\approx 4,3}\\end{array}\\]<br \/>\nPortanto,\u00a0\\({\\overline {AD} \\approx 4,3}\\) cm.<\/li>\n<\/ol><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14145' onClick='GTTabs_show(0,14145)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O quadril\u00e1tero [ABCD] est\u00e1 dividido em dois tri\u00e2ngulos ret\u00e2ngulos. Qual \u00e9 a medida da amplitude do \u00e2ngulo BAC, arredondada \u00e0s unidades?\u00a0Explica como chegaste \u00e0 tua resposta. Determina\u00a0\\(\\overline {AD} \\) arredondado \u00e0s&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14148,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,493,492],"series":[],"class_list":["post-14145","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-9--ano","category-aplicando","category-trigonometria-9--ano","tag-9-o-ano","tag-cosseno","tag-razao-trigonometrica","tag-tangente"],"views":2245,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag056-9a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14145","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=14145"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14145\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14148"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14145"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}