{"id":23500,"date":"2022-12-08T19:30:05","date_gmt":"2022-12-08T19:30:05","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=23500"},"modified":"2022-12-21T23:33:19","modified_gmt":"2022-12-21T23:33:19","slug":"um-lago","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=23500","title":{"rendered":"Um lago"},"content":{"rendered":"\n<p><ul id='GTTabs_ul_23500' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_23500' class='GTTabs_curr'><a  id=\"23500_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_23500' ><a  id=\"23500_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_23500'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23501\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23501\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9.png\" data-orig-size=\"530,390\" 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=\"8_Pag065-9\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9.png\" class=\"alignright wp-image-23501\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9-300x221.png\" alt=\"\" width=\"340\" height=\"250\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9-300x221.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9.png 530w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>Fixando uma estaca no ponto A e marcando os pontos C e D nas margens do lago, de modo que o \u00e2ngulo ADC seja reto, a Catarina verificou que \\(\\overline {DA} = 40\\) m e que \\(\\overline {AC} = 50\\).<\/p>\n<p>Qual \u00e9 a dist\u00e2ncia entre os pontos C e D das margens do lago?<\/p>\n<p>\u00a0<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_23500' onClick='GTTabs_show(1,23500)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_23500'>\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\/2022\/12\/8_Pag065-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"23501\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=23501\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9.png\" data-orig-size=\"530,390\" 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=\"8_Pag065-9\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9.png\" class=\"alignright wp-image-23501\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9-300x221.png\" alt=\"\" width=\"340\" height=\"250\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9-300x221.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9.png 530w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>Fixando uma estaca no ponto A e marcando os pontos C e D nas margens do lago, de modo que o \u00e2ngulo ADC seja reto, a Catarina verificou que \\(\\overline {DA} = 40\\) m e que \\(\\overline {AC} = 50\\).<\/p>\n<p>Qual \u00e9 a dist\u00e2ncia entre os pontos C e D das margens do lago?<\/p>\n<\/blockquote>\n<p>\u00a0<\/p>\n<p>Aplicando o Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [ACD], temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\overline {CD} }&amp; = &amp;{\\sqrt {{{\\overline {AC} }^2} &#8211; {{\\overline {AD} }^2}} }\\\\{}&amp; = &amp;{\\sqrt {{{50}^2} &#8211; {{40}^2}} }\\\\{}&amp; = &amp;{\\sqrt {2500 &#8211; 1600} }\\\\{}&amp; = &amp;{\\sqrt {900} }\\\\{}&amp; = &amp;{30}\\end{array}\\]<\/p>\n<p>\u00c9 de 30 metros a dist\u00e2ncia entre os pontos C e D das margens do lago.<\/p>\n<p>\u00a0<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_23500' onClick='GTTabs_show(0,23500)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Fixando uma estaca no ponto A e marcando os pontos C e D nas margens do lago, de modo que o \u00e2ngulo ADC seja reto, a Catarina verificou que \\(\\overline {DA}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":23502,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,682],"tags":[424,67,118],"series":[],"class_list":["post-23500","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-teorema-de-pitagoras","tag-8-o-ano","tag-geometria","tag-teorema-de-pitagoras"],"views":215,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2022\/12\/8_Pag065-9_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23500","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=23500"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/23500\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/23502"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=23500"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=23500"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=23500"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=23500"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}