{"id":14372,"date":"2018-04-11T00:07:44","date_gmt":"2018-04-10T23:07:44","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14372"},"modified":"2022-01-11T19:39:00","modified_gmt":"2022-01-11T19:39:00","slug":"um-muro-e-uma-escada","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14372","title":{"rendered":"Um muro e uma escada"},"content":{"rendered":"<p><ul id='GTTabs_ul_14372' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14372' class='GTTabs_curr'><a  id=\"14372_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14372' ><a  id=\"14372_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_14372'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14373\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14373\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2.png\" data-orig-size=\"522,458\" 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=\"Escada\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2.png\" class=\"alignright size-medium wp-image-14373\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2-300x263.png\" alt=\"\" width=\"300\" height=\"263\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2-300x263.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2.png 522w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Observa a figura.<br \/>\nO muro tem 5 m de altura e a escada tem 5,20 m de comprimento.<\/p>\n<ol>\n<li>Calcula:<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>A dist\u00e2ncia do p\u00e9 da escada ao muro.<br \/>\nEscreve essa dist\u00e2ncia arredondada \u00e0s d\u00e9cimas.<\/li>\n<li>A medida da amplitude, arredondada \u00e0s unidades, do \u00e2ngulo formado pela escada e pelo muro.<\/li>\n<\/ol>\n<ol start=\"2\">\n<li>Para que a escada n\u00e3o caia, o \u00e2ngulo que a escada e o muro fazem deve ter, no m\u00e1ximo, 65 graus. Determina, nesse caso, a altura, arredondada \u00e0s d\u00e9cimas, a que podemos colocar o topo da escada contra o muro.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14372' onClick='GTTabs_show(1,14372)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14372'>\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\/9V2Pag73-2.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14373\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14373\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2.png\" data-orig-size=\"522,458\" 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=\"Escada\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2.png\" class=\"alignright size-medium wp-image-14373\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2-300x263.png\" alt=\"\" width=\"300\" height=\"263\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2-300x263.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2.png 522w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Observa a figura.<br \/>\nO muro tem 5 m de altura e a escada tem 5,20 m de comprimento.<\/p>\n<\/blockquote>\n<ol>\n<li>Calcula:<\/li>\n<\/ol>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [<em>ABC<\/em>], temos:<br \/>\n\\[d = \\overline {AB} = \\sqrt {{{\\overline {AC} }^2} &#8211; {{\\overline {BC} }^2}} = \\sqrt {{{5,2}^2} &#8211; {5^2}} = \\sqrt {2,04} \\approx 1,4\\]<br \/>\nA dist\u00e2ncia do p\u00e9 da escada ao muro \u00e9, aproximadamente, 1,4 metros.<br \/>\n\u00ad<\/li>\n<li>No tri\u00e2ngulo\u00a0ret\u00e2ngulo [<em>ABC<\/em>], temos:<br \/>\n\\[\\begin{array}{*{20}{l}}{\\cos A\\widehat CB = \\frac{{\\overline {BC} }}{{\\overline {AC} }}}&amp; \\Leftrightarrow &amp;{\\cos A\\widehat CB = \\frac{5}{{5,2}}}\\\\{}&amp; \\Leftrightarrow &amp;{A\\widehat CB = {{\\cos }^{ &#8211; 1}}\\left( {\\frac{5}{{5,2}}} \\right)}\\\\{}&amp;{}&amp;{A\\widehat CB \\approx 16^\\circ }\\end{array}\\]<br \/>\n\u00c9 16 graus a medida da amplitude, arredondada \u00e0s unidades, do \u00e2ngulo formado pela escada e pelo muro.<br \/>\n\u00ad<\/li>\n<\/ol>\n<ol start=\"2\">\n<li>Na express\u00e3o acima, considerando\u00a0\\(A\\widehat CB = 65^\\circ \\), vem:<br \/>\n\\[\\begin{array}{*{20}{l}}{\\cos 65^\\circ = \\frac{h}{{\\overline {AC} }}}&amp; \\Leftrightarrow &amp;{\\cos 65^\\circ = \\frac{h}{{5,2}}}\\\\{}&amp; \\Leftrightarrow &amp;{h = 5,2 \\times \\cos 65^\\circ }\\\\{}&amp;{}&amp;{h \\approx 2,2}\\end{array}\\]<br \/>\nNesse caso, a altura, arredondada \u00e0s d\u00e9cimas, a que podemos colocar o topo da escada contra o muro \u00e9 2,2 metros, aproximadamente.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14372' onClick='GTTabs_show(0,14372)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa a figura. O muro tem 5 m de altura e a escada tem 5,20 m de comprimento. Calcula: A dist\u00e2ncia do p\u00e9 da escada ao muro. Escreve essa dist\u00e2ncia arredondada&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14375,"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],"series":[],"class_list":["post-14372","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"],"views":3388,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag73-2a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14372","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=14372"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14372\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14375"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14372"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14372"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14372"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14372"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}