{"id":14028,"date":"2018-03-10T20:57:11","date_gmt":"2018-03-10T20:57:11","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14028"},"modified":"2022-01-11T10:27:59","modified_gmt":"2022-01-11T10:27:59","slug":"a-instalacao-de-um-teleferico","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14028","title":{"rendered":"A instala\u00e7\u00e3o de um telef\u00e9rico"},"content":{"rendered":"<p><ul id='GTTabs_ul_14028' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14028' class='GTTabs_curr'><a  id=\"14028_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14028' ><a  id=\"14028_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_14028'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14031\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14031\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1.png\" data-orig-size=\"410,260\" 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=\"Telef\u00e9rico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1.png\" class=\"alignright wp-image-14031\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1-300x190.png\" alt=\"\" width=\"340\" height=\"216\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1-300x190.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1.png 410w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>O topo B da montanha est\u00e1 a 114 m de altitude.<br \/>\nPara instalar um telef\u00e9rico, foi medida a amplitude do \u00e2ngulo em A e o desn\u00edvel entre os pontos A e B.<\/p>\n<ol>\n<li>Qual \u00e9 a dist\u00e2ncia, arredondada \u00e0s cent\u00e9simas, entre os pontos A e B da montanha?<br \/>\nExplica a tua resposta.<\/li>\n<li>Devido ao peso do telef\u00e9rico, o seu cabo de a\u00e7o \u00e9 curvo.<br \/>\nEssa curvatura torna o comprimento do cabo 2% maior do que a dist\u00e2ncia entre os pontos de partida, A, e de chegada, B, do telef\u00e9rico.<br \/>\n<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14032\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14032\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png\" data-orig-size=\"410,260\" 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=\"Telef\u00e9rico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png\" class=\"alignright wp-image-14032\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2-300x190.png\" alt=\"\" width=\"340\" height=\"216\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2-300x190.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png 410w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>Qual \u00e9 o comprimento do cabo? Explica como chegaste \u00e0 tua resposta.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14028' onClick='GTTabs_show(1,14028)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14028'>\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\/9V2Pag052-12_1.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14031\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14031\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1.png\" data-orig-size=\"410,260\" 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=\"Telef\u00e9rico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1.png\" class=\"alignright size-medium wp-image-14031\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1-300x190.png\" alt=\"\" width=\"300\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1-300x190.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_1.png 410w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo, tem-se:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm sen}\\nolimits} 35^\\circ = \\frac{{114}}{{\\overline {AB} }}}&amp; \\Leftrightarrow &amp;{\\overline {AB} = \\frac{{114}}{{{\\mathop{\\rm sen}\\nolimits} 35^\\circ }}}\\\\{}&amp;{}&amp;{\\overline {AB} \\approx 198,75}\\end{array}\\]<br \/>\nA dist\u00e2ncia entre os pontos A e B \u00e9, aproximadamente, 198,75 metros.<br \/>\n\u00ad<\/li>\n<li>Ora, \\(\\overline {AB} \\times 1,02 \\approx 202,73\\).<br \/>\n<a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14032\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14032\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png\" data-orig-size=\"410,260\" 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=\"Telef\u00e9rico\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png\" class=\"alignright size-medium wp-image-14032\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2-300x190.png\" alt=\"\" width=\"300\" height=\"190\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2-300x190.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2.png 410w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Portanto, o cabo tem, aproximadamente, 201,73 metros de comprimento.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14028' onClick='GTTabs_show(0,14028)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O topo B da montanha est\u00e1 a 114 m de altitude. Para instalar um telef\u00e9rico, foi medida a amplitude do \u00e2ngulo em A e o desn\u00edvel entre os pontos A e&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14030,"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-14028","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":2724,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-12_2a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14028","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=14028"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14028\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14030"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14028"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14028"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14028"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14028"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}