{"id":14005,"date":"2018-03-10T00:43:23","date_gmt":"2018-03-10T00:43:23","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14005"},"modified":"2022-01-11T02:03:58","modified_gmt":"2022-01-11T02:03:58","slug":"uma-torre-retransmissora-de-televisao","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14005","title":{"rendered":"Uma torre retransmissora de televis\u00e3o"},"content":{"rendered":"<p><ul id='GTTabs_ul_14005' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14005' class='GTTabs_curr'><a  id=\"14005_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14005' ><a  id=\"14005_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_14005'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14006\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14006\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png\" data-orig-size=\"520,245\" 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=\"Avi\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png\" class=\"alignright wp-image-14006\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9-300x141.png\" alt=\"\" width=\"460\" height=\"217\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9-300x141.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9-720x340.png 720w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png 520w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><\/a>Um avi\u00e3o descola da pista no ponto A e sobe fazendo um \u00e2ngulo constante de 15 graus com o plano do ch\u00e3o.<br \/>\nNa dire\u00e7\u00e3o do percurso do avi\u00e3o, a 2 km do aeroporto, existe um torre retransmissora de televis\u00e3o com 40 metros de altura.<\/p>\n<p>Ser\u00e1 que \u00e9 necess\u00e1rio o avi\u00e3o desviar-se da rota para n\u00e3o embater nessa torre?<br \/>\nExplica a tua resposta.<br \/>\nA figura n\u00e3o est\u00e1 \u00e0 escala.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14005' onClick='GTTabs_show(1,14005)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14005'>\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\/9V2Pag052-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14006\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14006\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png\" data-orig-size=\"520,245\" 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=\"Avi\u00e3o\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png\" class=\"alignright wp-image-14006\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9-300x141.png\" alt=\"\" width=\"460\" height=\"217\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9-300x141.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9-720x340.png 720w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png 520w\" sizes=\"auto, (max-width: 460px) 100vw, 460px\" \/><\/a>Consideremos o tri\u00e2ngulo [ABC], ret\u00e2ngulo em B.<\/p>\n<p>Ora,<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} 15^\\circ = \\frac{{\\overline {BC} }}{{\\overline {AB} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 15^\\circ = \\frac{{\\overline {BC} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BC} = 2 \\times {\\mathop{\\rm tg}\\nolimits} 15^\\circ }\\\\{}&amp;{}&amp;{\\overline {BC} \\approx 0,536}\\end{array}\\]<\/p>\n<p>Como \\(\\overline {BC} \\approx 0,536\\;km &gt; 40\\;m\\), ent\u00e3o n\u00e3o \u00e9 necess\u00e1rio o avi\u00e3o desviar-se da rota para n\u00e3o embater nessa torre.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14005' onClick='GTTabs_show(0,14005)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Um avi\u00e3o descola da pista no ponto A e sobe fazendo um \u00e2ngulo constante de 15 graus com o plano do ch\u00e3o. Na dire\u00e7\u00e3o do percurso do avi\u00e3o, a 2 km&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14006,"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-14005","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":2812,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag052-9.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14005","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=14005"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14005\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14006"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14005"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}