{"id":14245,"date":"2018-04-02T15:40:00","date_gmt":"2018-04-02T14:40:00","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14245"},"modified":"2022-01-11T11:55:23","modified_gmt":"2022-01-11T11:55:23","slug":"a-largura-da-rua-onde-mora-o-rogerio","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14245","title":{"rendered":"A largura da rua onde mora o Rog\u00e9rio"},"content":{"rendered":"<p><ul id='GTTabs_ul_14245' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14245' class='GTTabs_curr'><a  id=\"14245_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14245' ><a  id=\"14245_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_14245'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14246\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14246\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png\" data-orig-size=\"600,395\" 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=\"Pr\u00e9dio\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png\" class=\"alignright wp-image-14246\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16-300x198.png\" alt=\"\" width=\"440\" height=\"290\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16-300x198.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png 600w\" sizes=\"auto, (max-width: 440px) 100vw, 440px\" \/><\/a>O Rog\u00e9rio encostou uma escada com 10 metros de comprimento a um pr\u00e9dio do lado esquerdo da sua rua, formando com o solo um \u00e2ngulo de 50 graus.<br \/>\nDepois, encostou-a a um pr\u00e9dio do lado direito da rua, sem alterar o ponto de apoio, formando com o solo um \u00e2ngulo de 60 graus.<\/p>\n<p>Qual \u00e9 o valor, arredondado \u00e0s d\u00e9cimas, da largura da rua onde mora o Rog\u00e9rio?<br \/>\nMostra como chegaste \u00e0 tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14245' onClick='GTTabs_show(1,14245)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14245'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14246\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14246\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png\" data-orig-size=\"600,395\" 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=\"Pr\u00e9dio\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png\" class=\"alignright wp-image-14246\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16-300x198.png\" alt=\"\" width=\"440\" height=\"290\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16-300x198.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16.png 600w\" sizes=\"auto, (max-width: 440px) 100vw, 440px\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo [<em>ABC<\/em>], vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\cos 50^\\circ = \\frac{{\\overline {AC} }}{{\\overline {BC} }}}&amp; \\Leftrightarrow &amp;{\\cos 50^\\circ = \\frac{{\\overline {AC} }}{{10}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AC} = 10 \\times \\cos 50^\\circ }\\end{array}\\]<\/p>\n<p>No tri\u00e2ngulo ret\u00e2ngulo [<em>CDE<\/em>], vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\cos 60^\\circ = \\frac{{\\overline {CD} }}{{\\overline {CE} }}}&amp; \\Leftrightarrow &amp;{\\cos 60^\\circ = \\frac{{\\overline {CD} }}{{10}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {CD} = 10 \\times \\cos 60^\\circ }\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {CD} = 10 \\times \\frac{1}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {CD} = 5}\\end{array}\\]<\/p>\n<p>A rua onde mora o Rodrigo tem, aproximadamente, 11,4 metros de largura:<\/p>\n<p>\\[\\overline {AD} = \\overline {AC} + \\overline {CD} = \\overline {AC} = 10 \\times \\cos 50^\\circ + 5 \\approx 11,4\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14245' onClick='GTTabs_show(0,14245)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Rog\u00e9rio encostou uma escada com 10 metros de comprimento a um pr\u00e9dio do lado esquerdo da sua rua, formando com o solo um \u00e2ngulo de 50 graus. Depois, encostou-a a&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14247,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,493,490,492],"series":[],"class_list":["post-14245","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-seno","tag-tangente"],"views":1838,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-16a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14245","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=14245"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14245\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14247"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14245"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14245"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14245"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}