{"id":14339,"date":"2018-04-10T00:23:25","date_gmt":"2018-04-09T23:23:25","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14339"},"modified":"2022-01-11T14:38:18","modified_gmt":"2022-01-11T14:38:18","slug":"um-prisma-triangular-reto","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14339","title":{"rendered":"Um prisma triangular reto"},"content":{"rendered":"<p><ul id='GTTabs_ul_14339' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14339' class='GTTabs_curr'><a  id=\"14339_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14339' ><a  id=\"14339_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_14339'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14340\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14340\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png\" data-orig-size=\"402,229\" 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=\"Prisma triangular\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png\" class=\"alignright size-medium wp-image-14340\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10-300x171.png\" alt=\"\" width=\"300\" height=\"171\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10-300x171.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png 402w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Na figura, est\u00e1 representado um prisma triangular reto [<em>ABCDEF<\/em>].<br \/>\nSabe-se que:<\/p>\n<ul>\n<li>o tri\u00e2ngulo [<em>ABC<\/em>] \u00e9 ret\u00e2ngulo em <em>A<\/em>;<\/li>\n<li>\\(\\overline {AC} = 2\\) cm;<\/li>\n<li>\\(\\overline {AE} = 6\\) cm;<\/li>\n<li>o volume do prisma \u00e9 42 cm<sup>3<\/sup>.<\/li>\n<\/ul>\n<ol>\n<li>Construiu-se um cubo com volume igual ao volume do prisma representado na figura.<br \/>\nQual \u00e9 a medida da aresta desse cubo, em cent\u00edmetros, arredondado \u00e0s d\u00e9cimas?<br \/>\n[A] 3,3<br \/>\n[B] 3,4<br \/>\n[C] 3,5<br \/>\n[D] 3,6]<\/li>\n<li>Determina a amplitude do \u00e2ngulo <em>ABC<\/em>.<br \/>\nApresenta o resultado em graus, arredondado \u00e0s unidades.<br \/>\nMostra como chegaste \u00e0 tua resposta.<\/li>\n<li>Identifica, usando as letras da figura, uma reta que seja concorrente com a reta <em>CB<\/em> e que n\u00e3o contenha qualquer aresta do prisma.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14339' onClick='GTTabs_show(1,14339)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14339'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<blockquote>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14340\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14340\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png\" data-orig-size=\"402,229\" 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=\"Prisma triangular\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png\" class=\"alignright size-medium wp-image-14340\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10-300x171.png\" alt=\"\" width=\"300\" height=\"171\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10-300x171.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10.png 402w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Na figura, est\u00e1 representado um prisma triangular reto [<em>ABCDEF<\/em>].<br \/>\nSabe-se que:<\/p>\n<\/blockquote>\n<ul>\n<li>\n<blockquote>\n<p>o tri\u00e2ngulo [<em>ABC<\/em>] \u00e9 ret\u00e2ngulo em <em>A<\/em>;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>\\(\\overline {AC} = 2\\) cm;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>\\(\\overline {AE} = 6\\) cm;<\/p>\n<\/blockquote>\n<\/li>\n<li>\n<blockquote>\n<p>o volume do prisma \u00e9 42 cm<sup>3<\/sup>.<\/p>\n<\/blockquote>\n<\/li>\n<\/ul>\n<ol>\n<li>Como \\(\\sqrt[3]{{42}} \\approx 3,476\\), ent\u00e3o a alternativa correta \u00e9 a [C].<br \/>\n[C] 3,5<br \/>\n\u00ad<\/li>\n<li>Comecemos por determinar\u00a0\\(\\overline {AB} \\):<br \/>\n\\[\\begin{array}{*{20}{l}}{{V_{Prisma}} = 42}&amp; \\Leftrightarrow &amp;{\\frac{{\\overline {AC} \\times \\overline {AB} }}{2} \\times \\overline {AE} = 42}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{{2 \\times \\overline {AB} }}{2} \\times 6 = 42}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AB} = 7}\\end{array}\\]<br \/>\nNo tri\u00e2ngulo ret\u00e2ngulo [<em>ABC<\/em>], vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} A\\widehat BC = \\frac{{\\overline {AC} }}{{\\overline {AB} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} A\\widehat BC = \\frac{2}{7}}\\\\{}&amp; \\Leftrightarrow &amp;{A\\widehat BC = {{{\\mathop{\\rm tg}\\nolimits} }^{ &#8211; 1}}\\left( {\\frac{2}{7}} \\right)}\\\\{}&amp;{}&amp;{A\\widehat BC \\approx 16^\\circ }\\end{array}\\]<\/li>\n<li>A reta <em>CF<\/em>, por exemplo.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14339' onClick='GTTabs_show(0,14339)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Na figura, est\u00e1 representado um prisma triangular reto [ABCDEF]. Sabe-se que: o tri\u00e2ngulo [ABC] \u00e9 ret\u00e2ngulo em A; \\(\\overline {AC} = 2\\) cm; \\(\\overline {AE} = 6\\) cm; o volume do&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14341,"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-14339","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":13732,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag70-10a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14339","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=14339"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14339\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14341"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14339"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14339"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14339"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}