{"id":14181,"date":"2018-03-30T19:42:52","date_gmt":"2018-03-30T18:42:52","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14181"},"modified":"2022-01-11T11:25:30","modified_gmt":"2022-01-11T11:25:30","slug":"a-area-de-um-triangulo-2","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14181","title":{"rendered":"A \u00e1rea de um tri\u00e2ngulo"},"content":{"rendered":"<p><ul id='GTTabs_ul_14181' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14181' class='GTTabs_curr'><a  id=\"14181_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14181' ><a  id=\"14181_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_14181'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14182\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14182\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4.png\" data-orig-size=\"390,220\" 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\/03\/9V2Pag60-4.png\" class=\"alignright size-medium wp-image-14182\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4-300x169.png\" alt=\"\" width=\"300\" height=\"169\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4-300x169.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4.png 390w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Calcula o valor exato da \u00e1rea, em cent\u00edmetros quadrados, do tri\u00e2ngulo ret\u00e2ngulo [<em>ABC<\/em>] da figura.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14181' onClick='GTTabs_show(1,14181)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14181'>\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\/03\/9V2Pag60-4.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14182\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14182\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4.png\" data-orig-size=\"390,220\" 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\/03\/9V2Pag60-4.png\" class=\"alignright size-medium wp-image-14182\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4-300x169.png\" alt=\"\" width=\"300\" height=\"169\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4-300x169.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4.png 390w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>No tri\u00e2ngulo ret\u00e2ngulo [<em>ABC<\/em>], vem \\({\\mathop{\\rm tg}\\nolimits} B\\widehat AC = \\frac{{\\overline {BC} }}{{\\overline {AB} }}\\), donde:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} 60^\\circ = \\frac{{8\\sqrt 3 }}{{\\overline {AB} }}}&amp; \\Leftrightarrow &amp;{\\sqrt 3 = \\frac{{8\\sqrt 3 }}{{\\overline {AB} }}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AB} = 8}\\end{array}\\]<\/p>\n<p>Logo, em cent\u00edmetros quadrados, a \u00e1rea do tri\u00e2ngulo [<em>ABC<\/em>] \u00e9:<\/p>\n<p>\\[{A_{\\left[ {ABC} \\right]}} = \\frac{{\\overline {AB} \\times \\overline {BC} }}{2} = \\frac{{8 \\times 8\\sqrt 3 }}{2} = 32\\sqrt 3 \\]<\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14181' onClick='GTTabs_show(0,14181)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Calcula o valor exato da \u00e1rea, em cent\u00edmetros quadrados, do tri\u00e2ngulo ret\u00e2ngulo [ABC] da figura. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14184,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[213,97,489],"tags":[426,493,492],"series":[],"class_list":["post-14181","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-razao-trigonometrica","tag-tangente"],"views":2540,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/9V2Pag60-4a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14181","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=14181"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14181\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14184"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14181"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14181"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}