{"id":14238,"date":"2018-04-01T19:59:53","date_gmt":"2018-04-01T18:59:53","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14238"},"modified":"2022-01-11T11:53:43","modified_gmt":"2022-01-11T11:53:43","slug":"a-area-do-triangulo-abc","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14238","title":{"rendered":"A \u00e1rea do tri\u00e2ngulo [ABC]"},"content":{"rendered":"<p><ul id='GTTabs_ul_14238' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14238' class='GTTabs_curr'><a  id=\"14238_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14238' ><a  id=\"14238_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_14238'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14239\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14239\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png\" data-orig-size=\"435,235\" 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\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png\" class=\"alignright size-medium wp-image-14239\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15-300x162.png\" alt=\"\" width=\"300\" height=\"162\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15-300x162.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png 435w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Observa a figura.<br \/>\nSabe-se que \\({\\mathop{\\rm sen}\\nolimits} \\alpha = 0,6\\).<\/p>\n<p>Qual \u00e9 a \u00e1rea, em cent\u00edmetros quadrados, do tri\u00e2ngulo [<em>ABC<\/em>] da figura?<br \/>\nApresenta todos os c\u00e1lculos que efetuares.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14238' onClick='GTTabs_show(1,14238)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14238'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14239\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14239\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png\" data-orig-size=\"435,235\" 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\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png\" class=\"alignright size-medium wp-image-14239\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15-300x162.png\" alt=\"\" width=\"300\" height=\"162\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15-300x162.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15.png 435w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo [<em>CDE<\/em>], vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm sen}\\nolimits} \\alpha = 0,6}&amp; \\Leftrightarrow &amp;{\\frac{{\\overline {ED} }}{{25}} = 0,6}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {ED} = 15}\\end{array}\\]<\/p>\n<p>Por aplica\u00e7\u00e3o do Teorema de Pit\u00e1goras no tri\u00e2ngulo ret\u00e2ngulo [<em>CDE<\/em>], vem:<\/p>\n<p>\\[\\overline {CD} = \\sqrt {{{\\overline {CE} }^2} &#8211; {{\\overline {DE} }^2}} = \\sqrt {{{25}^2} &#8211; {{15}^2}} = \\sqrt {400} = 20\\]<\/p>\n<p>Como os tri\u00e2ngulos [<em>CDE<\/em>] e [<em>ABC<\/em>] s\u00e3o semelhantes, vem:<\/p>\n<p>\\[A{}_{\\left[ {ABC} \\right]} = {\\left( {\\frac{{\\overline {AC} }}{{\\overline {CD} }}} \\right)^2} \\times {A_{\\left[ {CDE} \\right]}} = {\\left( {\\frac{{36}}{{20}}} \\right)^2} \\times \\frac{{\\overline {CD} \\times \\overline {DE} }}{2} = \\frac{{81}}{{25}} \\times \\frac{{20 \\times 15}}{2} = 486\\]<\/p>\n<p>Portanto, o tri\u00e2ngulo [<em>ABC<\/em>] tem 486 cm<sup>2<\/sup> de \u00e1rea.<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14238' onClick='GTTabs_show(0,14238)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa a figura. Sabe-se que \\({\\mathop{\\rm sen}\\nolimits} \\alpha = 0,6\\). Qual \u00e9 a \u00e1rea, em cent\u00edmetros quadrados, do tri\u00e2ngulo [ABC] da figura? Apresenta todos os c\u00e1lculos que efetuares. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14240,"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-14238","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":2376,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag62-15a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14238","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=14238"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14238\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14240"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14238"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14238"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}