{"id":14333,"date":"2018-04-09T23:16:48","date_gmt":"2018-04-09T22:16:48","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14333"},"modified":"2022-01-11T14:34:45","modified_gmt":"2022-01-11T14:34:45","slug":"uma-rampa-de-skate","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14333","title":{"rendered":"Uma rampa de <em>skate<\/em>"},"content":{"rendered":"<p><ul id='GTTabs_ul_14333' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14333' class='GTTabs_curr'><a  id=\"14333_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14333' ><a  id=\"14333_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_14333'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14334\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14334\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9.png\" data-orig-size=\"536,204\" 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=\"Rampa de skate\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9.png\" class=\"alignright wp-image-14334\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9-300x114.png\" alt=\"\" width=\"340\" height=\"129\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9-300x114.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9-1320x500.png 1320w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9.png 536w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>A figura representa um modelo geom\u00e9trico de uma rampa de <em>skate<\/em>.<br \/>\nO modelo n\u00e3o est\u00e1 desenhado \u00e0 escala.<br \/>\nEste modelo \u00e9 um s\u00f3lido que pode ser decomposto no cubo [<em>ABCDEFIJ<\/em>] e nos prismas triangulares retos [<em>BHIFAG<\/em>] e [<em>CKJEDL<\/em>], geometricamente iguais. As bases dos prismas s\u00e3o tri\u00e2ngulos ret\u00e2ngulos.<br \/>\nSabe-se ainda que:<\/p>\n<ul>\n<li>\\(\\overline {HI} = 5\\) m;<\/li>\n<li>\\(I\\widehat HB = 32^\\circ \\).<\/li>\n<\/ul>\n<ol>\n<li>Identifica, usando as letras da figura, a interse\u00e7\u00e3o dos planos <em>HIB<\/em> e <em>JCD<\/em>.<\/li>\n<li>Determina o volume do s\u00f3lido representado na figura.<br \/>\nApresenta o resultado em metros c\u00fabicos, arredondado \u00e0s unidades.<br \/>\nApresenta os c\u00e1lculos que efetuares.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14333' onClick='GTTabs_show(1,14333)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14333'>\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\/04\/9V2Pag70-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14334\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14334\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9.png\" data-orig-size=\"536,204\" 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=\"Rampa de skate\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9.png\" class=\"alignright wp-image-14334\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9-300x114.png\" alt=\"\" width=\"340\" height=\"129\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9-300x114.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9-1320x500.png 1320w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9.png 536w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>A interse\u00e7\u00e3o dos planos <em>HIB<\/em> e <em>JCD<\/em> \u00e9 a reta <em>CJ<\/em>.<br \/>\n\u00ad<\/li>\n<li>No tri\u00e2ngulo ret\u00e2ngulo [BHI], vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} I\\widehat HB = \\frac{{\\overline {BI} }}{{\\overline {HI} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 32^\\circ = \\frac{{\\overline {BI} }}{5}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BI} = 5 \\times {\\mathop{\\rm tg}\\nolimits} 32^\\circ }\\end{array}\\]<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{S\u00f3lido}}}&amp; = &amp;{{V_{Cubo}} + 2 \\times {V_{Prisma}}}\\\\{}&amp; = &amp;{{{\\left( {\\overline {BI} } \\right)}^3} + 2 \\times \\frac{{\\overline {HI} \\times \\overline {BI} }}{2} \\times \\overline {AB} }\\\\{}&amp; = &amp;{{{\\left( {5 \\times {\\mathop{\\rm tg}\\nolimits} 32^\\circ } \\right)}^3} + 2 \\times \\frac{{5 \\times 5 \\times {\\mathop{\\rm tg}\\nolimits} 32^\\circ }}{2} \\times 5 \\times {\\mathop{\\rm tg}\\nolimits} 32^\\circ }\\\\{}&amp; = &amp;{{{\\left( {5 \\times {\\mathop{\\rm tg}\\nolimits} 32^\\circ } \\right)}^3} + 5 \\times {{\\left( {5 \\times {\\mathop{\\rm tg}\\nolimits} 32^\\circ } \\right)}^2}}\\\\{}&amp; \\approx &amp;{79}\\end{array}\\]<br \/>\nO s\u00f3lido representado na figura tem, aproximadamente, 79 metros c\u00fabicos de volume.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14333' onClick='GTTabs_show(0,14333)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado A figura representa um modelo geom\u00e9trico de uma rampa de skate. O modelo n\u00e3o est\u00e1 desenhado \u00e0 escala. Este modelo \u00e9 um s\u00f3lido que pode ser decomposto no cubo [ABCDEFIJ] e&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14335,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,491,493,490,492,109],"series":[],"class_list":["post-14333","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-cosseno","tag-razao-trigonometrica","tag-seno","tag-tangente","tag-volume"],"views":3209,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-9a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14333","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=14333"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14333\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14335"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14333"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14333"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14333"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}