{"id":14012,"date":"2018-03-10T12:29:14","date_gmt":"2018-03-10T12:29:14","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14012"},"modified":"2022-01-11T02:13:18","modified_gmt":"2022-01-11T02:13:18","slug":"o-monumento-do-cristo-rei","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14012","title":{"rendered":"O monumento do Cristo Rei"},"content":{"rendered":"<p><ul id='GTTabs_ul_14012' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14012' class='GTTabs_curr'><a  id=\"14012_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14012' ><a  id=\"14012_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_14012'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14013\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14013\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b.png\" data-orig-size=\"593,529\" 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=\"Cristo Rei\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b-300x268.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b.png\" class=\"alignright size-medium wp-image-14013\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b-300x268.png\" alt=\"\" width=\"300\" height=\"268\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b-300x268.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b.png 593w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>O monumento do <a href=\"https:\/\/pt.wikipedia.org\/wiki\/Santu%C3%A1rio_Nacional_de_Cristo_Rei\" target=\"_blank\" rel=\"noopener\">Cristo Rei<\/a> foi <a href=\"https:\/\/www.youtube.com\/watch?v=0y8gJv95sLM\" target=\"_blank\" rel=\"noopener\">inaugurado<\/a> a 17 de maio de 1959.<br \/>\n\u00c9 composto por um pedestal, com 82 m de altura, e pela est\u00e1tua, com 28 m de altura.<\/p>\n<ol>\n<li>No momento em que o sol incide na est\u00e1tua, fazendo com ela um \u00e2ngulo de 50 graus, quanto mede o comprimento da sombra do monumento?<\/li>\n<li>H\u00e1 momentos do dia em que a sombra de um objeto \u00e9 igual \u00e0 sua altura. Qual \u00e9 a amplitude do \u00e2ngulo que os raios solares fazem com a est\u00e1tua nos momentos referidos?<br \/>\nJustifica a tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14012' onClick='GTTabs_show(1,14012)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14012'>\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\/9V2Pag052-10b.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14013\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14013\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b.png\" data-orig-size=\"593,529\" 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=\"Cristo Rei\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b-300x268.png\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b.png\" class=\"alignright wp-image-14013\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b-300x268.png\" alt=\"\" width=\"360\" height=\"321\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b-300x268.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-10b.png 593w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/a>Considerando o tri\u00e2ngulo ret\u00e2ngulo [ABC], vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} 50^\\circ = \\frac{{\\overline {BC} }}{{\\overline {AB} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 50^\\circ = \\frac{{\\overline {BC} }}{{82 + 28}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BC} = 110 \\times {\\mathop{\\rm tg}\\nolimits} 50^\\circ }\\\\{}&amp;{}&amp;{\\overline {BC} \\approx 131}\\end{array}\\]<br \/>\nA sombra do monumento tem, aproximadamente, 131 metros de comprimento.<br \/>\n\u00ad<\/li>\n<li>Para o comprimento da sombra de um objeto ser igual \u00e0 sua altura, a amplitude do \u00e2ngulo que os raios solares fazem com o objeto deve ser de 45 graus, pois nesse caso o tri\u00e2ngulo ret\u00e2ngulo [ABC] seria tamb\u00e9m is\u00f3sceles: \\(\\overline {AB} = \\overline {BC} \\).<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14012' onClick='GTTabs_show(0,14012)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O monumento do Cristo Rei foi inaugurado a 17 de maio de 1959. \u00c9 composto por um pedestal, com 82 m de altura, e pela est\u00e1tua, com 28 m de altura.&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14015,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,493,492],"series":[],"class_list":["post-14012","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-tangente"],"views":2867,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/CristoReiInaugurado1959.jpg","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14012","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=14012"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14012\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14015"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14012"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14012"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14012"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14012"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}