{"id":14172,"date":"2018-03-30T17:08:25","date_gmt":"2018-03-30T16:08:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14172"},"modified":"2022-01-11T11:21:59","modified_gmt":"2022-01-11T11:21:59","slug":"uma-escada-magirus","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14172","title":{"rendered":"Uma escada magirus"},"content":{"rendered":"<p><ul id='GTTabs_ul_14172' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14172' class='GTTabs_curr'><a  id=\"14172_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14172' ><a  id=\"14172_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_14172'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14173\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14173\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3.png\" data-orig-size=\"400,315\" 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=\"Escada magirus\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3.png\" class=\"alignright size-medium wp-image-14173\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3-300x236.png\" alt=\"\" width=\"300\" height=\"236\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3-300x236.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3.png 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Numa opera\u00e7\u00e3o de salvamento, aquando de um inc\u00eandio num pr\u00e9dio de v\u00e1rios andares, foi utilizada uma escada <em>magirus<\/em>, com 30 metros de comprimento, assente num cami\u00e3o a 2,5 metros do ch\u00e3o.<\/p>\n<p>De acordo com os bombeiros, a inclina\u00e7\u00e3o m\u00e1xima da escada \u00e9 60 graus.<\/p>\n<p>Qual \u00e9 a altura m\u00e1xima, arredondada \u00e0s cent\u00e9simas, que a escada pode atingir? Explica como chegaste \u00e0 tua resposta.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14172' onClick='GTTabs_show(1,14172)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14172'>\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\/03\/9V2Pag60-3.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14173\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14173\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3.png\" data-orig-size=\"400,315\" 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=\"Escada magirus\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3.png\" class=\"alignright size-medium wp-image-14173\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3-300x236.png\" alt=\"\" width=\"300\" height=\"236\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3-300x236.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3.png 400w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo [ABC], vem \\({\\mathop{\\rm sen}\\nolimits} B\\widehat AC = \\frac{{\\overline {BC} }}{{\\overline {AB} }}\\), donde:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm sen}\\nolimits} 60^\\circ = \\frac{{\\overline {BC} }}{{30}}}&amp; \\Leftrightarrow &amp;{\\frac{{\\sqrt 3 }}{2} = \\frac{{\\overline {BC} }}{{30}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BC} = \\frac{{30\\sqrt 3 }}{2}}\\end{array}\\]<\/p>\n<p>Logo,\u00a0a altura m\u00e1xima que a escada pode atingir \u00e9, aproximadamente, \\({h_{m\u00e1x}} = \\overline {BC} + \\overline {DE} = \\frac{{30\\sqrt 3 }}{2} + 2,5 \\approx 28,48\\)\u00a0 metros.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14172' onClick='GTTabs_show(0,14172)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Numa opera\u00e7\u00e3o de salvamento, aquando de um inc\u00eandio num pr\u00e9dio de v\u00e1rios andares, foi utilizada uma escada magirus, com 30 metros de comprimento, assente num cami\u00e3o a 2,5 metros do ch\u00e3o.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14175,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,493,490],"series":[],"class_list":["post-14172","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-razao-trigonometrica","tag-seno"],"views":2524,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-3a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14172","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=14172"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14172\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14175"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14172"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}