{"id":23542,"date":"2022-12-09T09:47:38","date_gmt":"2022-12-09T09:47:38","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23542"},"modified":"2022-12-21T23:35:51","modified_gmt":"2022-12-21T23:35:51","slug":"uma-torre-torta","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23542","title":{"rendered":"Uma torre &#8220;torta&#8221;"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23542' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23542' class='GTTabs_curr'><a  id=\"23542_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23542' ><a  id=\"23542_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_23542'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Quem chega a Lisboa, entrando pelo Tejo, encontra uma torre &#8220;torta&#8221;, mas elegante, que alberga o <a href=\"https:\/\/www.portodelisboa.pt\/vts\" target=\"_blank\" rel=\"noopener\">Centro de Coordena\u00e7\u00e3o e Controlo de Tr\u00e1fego Mar\u00edtimo<\/a>.<\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23545\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23545\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png\" data-orig-size=\"467,334\" 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_Pag066-14A\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png\" class=\"aligncenter wp-image-23545\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A-300x215.png\" alt=\"\" width=\"320\" height=\"229\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A-300x215.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png 467w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<p>A torre tem a forma de um prisma quadrangular obl\u00edquo. A sua altura \u00e9 de 36 m, e a torre est\u00e1 inclinada a sul, segundo um \u00e2ngulo de cerca de 75\u00b0. Se o sol incidisse a pique sobre a torre, esta projetaria uma sombra retangular, em que um dos lados mediria, aproximadamente, 9,6 m, como est\u00e1 representado na figura.<\/p>\n<ol>\n<li><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23547\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23547\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png\" data-orig-size=\"299,310\" 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_Pag066-14B\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png\" class=\"alignright wp-image-23547\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B-289x300.png\" alt=\"\" width=\"200\" height=\"207\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B-289x300.png 289w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png 299w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>Qual \u00e9 a medida do comprimento &#8211; <em>h<\/em> &#8211; da torre?<br \/>Apresenta todos os c\u00e1lculos que efetuares e indica o resultado, em metros, aproximado \u00e0s unidades.<\/li>\n<li>A face [ABCD] da torre tem a forma de um paralelogramo.<br \/>Indica a amplitude do \u00e2ngulo \u03b1.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23542' onClick='GTTabs_show(1,23542)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23542'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p>Quem chega a Lisboa, entrando pelo Tejo, encontra uma torre &#8220;torta&#8221;, mas elegante, que alberga o Centro de Coordena\u00e7\u00e3o e Controlo de Tr\u00e1fego Mar\u00edtimo.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23545\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23545\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png\" data-orig-size=\"467,334\" 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_Pag066-14A\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png\" class=\"aligncenter wp-image-23545\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A-300x215.png\" alt=\"\" width=\"320\" height=\"229\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A-300x215.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A.png 467w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/a><\/p>\n<blockquote>\n<p>A torre tem a forma de um prisma quadrangular obl\u00edquo. A sua altura \u00e9 de 36 m, e a torre est\u00e1 inclinada a sul, segundo um \u00e2ngulo de cerca de 75\u00b0. Se o sol incidisse a pique sobre a torre, esta projetaria uma sombra retangular, em que um dos lados mediria, aproximadamente, 9,6 m, como est\u00e1 representado na figura.<\/p>\n<\/blockquote>\n<ol>\n<li>\n<blockquote><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23547\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23547\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png\" data-orig-size=\"299,310\" 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_Pag066-14B\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png\" class=\"alignright wp-image-23547\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B-289x300.png\" alt=\"\" width=\"200\" height=\"207\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B-289x300.png 289w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14B.png 299w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/><\/a>Qual \u00e9 a medida do comprimento &#8211; <em>h<\/em> &#8211; da torre?<br \/>Apresenta todos os c\u00e1lculos que efetuares e indica o resultado, em metros, aproximado \u00e0s unidades.<\/blockquote>\n<\/li>\n<li>\n<blockquote>A face [ABCD] da torre tem a forma de um paralelogramo.<br \/>Indica a amplitude do \u00e2ngulo \u03b1.<\/blockquote>\n<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<ol>\n<li>Aplicando o Teorema de Pit\u00e1goras, vem:<br \/>\\[h = \\sqrt {{{36}^2} + {{9,6}^2}} = \\sqrt {1296 + 92,16} = \\sqrt {1388,16} \\approx 37\\]<br \/>Portanto, o comprimento &#8211; <em>h<\/em> &#8211; da torre \u00e9, aproximadamente, 37 metros.<br \/><br \/><\/li>\n<li>A amplitude do \u00e2ngulo \u03b1 \u00e9 \\(180^\\circ &#8211; 75^\\circ = 115^\\circ \\), pois os \u00e2ngulos assinalados na figura s\u00e3o \u00e2ngulos de lados inversamente paralelos.<\/li>\n<\/ol>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23542' onClick='GTTabs_show(0,23542)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Quem chega a Lisboa, entrando pelo Tejo, encontra uma torre &#8220;torta&#8221;, mas elegante, que alberga o Centro de Coordena\u00e7\u00e3o e Controlo de Tr\u00e1fego Mar\u00edtimo. A torre tem a forma de um&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23546,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,118],"series":[],"class_list":["post-23542","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-teorema-de-pitagoras"],"views":424,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag066-14A_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23542","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=23542"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23542\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23546"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23542"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}