{"id":13105,"date":"2017-11-28T21:11:43","date_gmt":"2017-11-28T21:11:43","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=13105"},"modified":"2022-01-17T23:21:11","modified_gmt":"2022-01-17T23:21:11","slug":"um-triangulo-retangulo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=13105","title":{"rendered":"Um tri\u00e2ngulo ret\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_13105' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_13105' class='GTTabs_curr'><a  id=\"13105_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_13105' ><a  id=\"13105_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_13105'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13106\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13106\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9.png\" data-orig-size=\"650,339\" 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=\"Tri\u00e2ngulo ret\u00e2ngulo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9.png\" class=\"alignright wp-image-13106\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9-300x156.png\" alt=\"\" width=\"400\" height=\"209\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9-300x156.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9.png 650w\" sizes=\"auto, (max-width: 400px) 100vw, 400px\" \/><\/a>O segmento de reta [AH] \u00e9 uma altura do tri\u00e2ngulo [ABC] ret\u00e2ngulo em A.<\/p>\n<p>Determina o valor da altura h.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_13105' onClick='GTTabs_show(1,13105)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_13105'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9resol.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"13107\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=13107\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9resol.png\" data-orig-size=\"1018,486\" 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=\"Tri\u00e2ngulos semelhantes\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9resol.png\" class=\"aligncenter wp-image-13107\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9resol.png\" alt=\"\" width=\"800\" height=\"382\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9resol.png 1018w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9resol-300x143.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/pag101-9resol-768x367.png 768w\" sizes=\"auto, (max-width: 800px) 100vw, 800px\" \/><\/a><\/p>\n<p>No tri\u00e2ngulo ret\u00e2ngulo [ABC], a altura [AH], relativamente \u00e0 hipotenusa [BC], divide-o em dois tri\u00e2ngulos ret\u00e2ngulos semelhantes, [ABH] e [ACH], conforme est\u00e1 ilustrado na figura acima.<\/p>\n<p>Tendo em considera\u00e7\u00e3o que, em tri\u00e2ngulos semelhantes, os lados correspondentes possuem comprimentos diretamente proporcionais, vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{\\frac{{\\overline {BH} }}{{\\overline {AH} }} = \\frac{{\\overline {AH} }}{{\\overline {CH} }}}&amp; \\Leftrightarrow &amp;{\\frac{{16}}{{\\overline {AH} }} = \\frac{{\\overline {AH} }}{{25}}}\\\\{}&amp; \\Leftrightarrow &amp;{{{\\overline {AH} }^2} = 400}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AH} = 20}\\end{array}\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_13105' onClick='GTTabs_show(0,13105)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O segmento de reta [AH] \u00e9 uma altura do tri\u00e2ngulo [ABC] ret\u00e2ngulo em A. Determina o valor da altura h. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":20546,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[100,97,187],"tags":[426,326],"series":[],"class_list":["post-13105","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-8--ano","category-aplicando","category-lugares-geometricos","tag-9-o-ano","tag-triangulos-semelhantes"],"views":3141,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2017\/11\/9V1Pag101_LG-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\/13105","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=13105"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/13105\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20546"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=13105"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=13105"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=13105"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=13105"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}