{"id":14251,"date":"2018-04-03T16:00:55","date_gmt":"2018-04-03T15:00:55","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14251"},"modified":"2022-01-11T13:44:41","modified_gmt":"2022-01-11T13:44:41","slug":"a-altura-da-parede","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14251","title":{"rendered":"A altura da parede"},"content":{"rendered":"<p><ul id='GTTabs_ul_14251' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14251' class='GTTabs_curr'><a  id=\"14251_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14251' ><a  id=\"14251_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_14251'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14252\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14252\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17.png\" data-orig-size=\"380,480\" 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=\"Parede\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17.png\" class=\"alignright size-medium wp-image-14252\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17-238x300.png\" alt=\"\" width=\"238\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17-238x300.png 238w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17.png 380w\" sizes=\"auto, (max-width: 238px) 100vw, 238px\" \/><\/a>O Gon\u00e7alo est\u00e1 a 2 m de uma parede, v\u00ea o seu topo segundo um \u00e2ngulo de 45 graus e a sua base segundo um \u00e2ngulo de 30 graus.<\/p>\n<p>Determina a altura dessa parede.<br \/>\nApresenta o resultado arredondado \u00e0s d\u00e9cimas.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14251' onClick='GTTabs_show(1,14251)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14251'>\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\/9V2Pag63-17.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14252\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14252\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17.png\" data-orig-size=\"380,480\" 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=\"Parede\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17.png\" class=\"alignright size-medium wp-image-14252\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17-238x300.png\" alt=\"\" width=\"238\" height=\"300\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17-238x300.png 238w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17.png 380w\" sizes=\"auto, (max-width: 238px) 100vw, 238px\" \/><\/a>Nos tri\u00e2ngulos ret\u00e2ngulos [<em>ABC<\/em>] e [<em>BCD<\/em>], temos:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} A\\widehat CB = \\frac{{\\overline {AB} }}{{\\overline {BC} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 30^\\circ = \\frac{{\\overline {AB} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{{\\sqrt 3 }}{3} = \\frac{{\\overline {AB} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {AB} = \\frac{{2\\sqrt 3 }}{3}}\\end{array}\\]e<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm tg}\\nolimits} B\\widehat CD = \\frac{{\\overline {BD} }}{{\\overline {BC} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm tg}\\nolimits} 45^\\circ = \\frac{{\\overline {BD} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{1 = \\frac{{\\overline {BD} }}{2}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BD} = 2}\\end{array}\\]<\/p>\n<p>\u00ad<br \/>\nA parede tem, aproximadamente, 3,2 metros de altura:<\/p>\n<p>\\[h = \\overline {AB} + \\overline {BD} = \\frac{{2\\sqrt 3 }}{3} + 2 \\approx 3,2\\]<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14251' onClick='GTTabs_show(0,14251)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Gon\u00e7alo est\u00e1 a 2 m de uma parede, v\u00ea o seu topo segundo um \u00e2ngulo de 45 graus e a sua base segundo um \u00e2ngulo de 30 graus. Determina a&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":14253,"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-14251","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":1911,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-17a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14251","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=14251"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14251\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14253"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14251"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14251"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14251"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14251"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}