{"id":3222,"date":"2010-09-29T17:00:02","date_gmt":"2010-09-29T16:00:02","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=3222"},"modified":"2022-01-21T01:28:06","modified_gmt":"2022-01-21T01:28:06","slug":"a-distancia-da-porta-a-estatua","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=3222","title":{"rendered":"A dist\u00e2ncia da porta \u00e0 est\u00e1tua"},"content":{"rendered":"<p><ul id='GTTabs_ul_3222' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_3222' class='GTTabs_curr'><a  id=\"3222_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_3222' ><a  id=\"3222_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_3222'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3225\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3225\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua.jpg\" data-orig-size=\"434,303\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&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;}\" data-image-title=\"Escola-Est\u00e1tua\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua.jpg\" class=\"alignright wp-image-3225\" title=\"Escola-Est\u00e1tua\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua-300x209.jpg\" alt=\"\" width=\"340\" height=\"237\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua-300x209.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua-150x104.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua-400x279.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua.jpg 434w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/a>O Jo\u00e3o e a Maria pretendem determinar a dist\u00e2ncia da porta A da sua escola \u00e0 est\u00e1tua E.<\/p>\n<p>Para isso, espetaram no jardim da escola uma estaca B, a 34 metros de A, e determinaram as amplitudes dos \u00e2ngulos EAB e ABE, sendo:<\/p>\n<ul>\n<li>$E\\widehat{A}B=26{}^\\text{o}$<\/li>\n<li>$E\\widehat{B}A=123{}^\\text{o}$<\/li>\n<\/ul>\n<p>Qual \u00e9 o valor da dist\u00e2ncia pretendida?<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_3222' onClick='GTTabs_show(1,3222)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_3222'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"3228\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=3228\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2.jpg\" data-orig-size=\"860,310\" 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;}\" data-image-title=\"Escola-Est\u00e1tua 2\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2.jpg\" class=\"alignright wp-image-3228\" title=\"Escola-Est\u00e1tua 2\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2-300x108.jpg\" alt=\"\" width=\"500\" height=\"180\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2-300x108.jpg 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2-150x54.jpg 150w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2-400x144.jpg 400w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/escolaestatua2.jpg 860w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a>Na figura ao lado,<\/p>\n<ul>\n<li>B&#8217; \u00e9 a proje\u00e7\u00e3o ortogonal do ponto B sobre o segmento de reta [EA];<\/li>\n<li>$x=\\overline{AB&#8217;}$;<\/li>\n<li>$y=\\overline{B&#8217;E}$;<\/li>\n<li>$h=\\overline{BB&#8217;}$;<\/li>\n<li>$B\\widehat{E}A=180{}^\\text{o}-(123{}^\\text{o}+26{}^\\text{o})=31{}^\\text{o}$.<\/li>\n<\/ul>\n<p>Desta forma, obt\u00e9m-se sucessivamente: \\[\\begin{matrix}<br \/>\ntg\\ 26{}^\\text{o}=\\frac{h}{x} &amp; \\Leftrightarrow\u00a0 &amp; h=x\\times tg\\ 26{}^\\text{o}\u00a0 \\\\<br \/>\n\\end{matrix}\\] \\[\\begin{matrix}<br \/>\n\\cos \\ 26{}^\\text{o}=\\frac{x}{34} &amp; \\Leftrightarrow\u00a0 &amp; x=34\\cos \\ 26{}^\\text{o}\u00a0 \\\\<br \/>\n\\end{matrix}\\] \\[\\begin{matrix}<br \/>\ntg\\ 31{}^\\text{o}=\\frac{h}{y} &amp; \\Leftrightarrow\u00a0 &amp; y=\\frac{h}{tg\\ 31{}^\\text{o}}\u00a0 \\\\<br \/>\n\\end{matrix}\\]<\/p>\n<p>Logo, $h=34\\cos 26{}^\\text{o}\\times tg\\ 26{}^\\text{o}$.<\/p>\n<p>Assim, \\[\\begin{array}{*{35}{l}}<br \/>\n\\overline{AE} &amp; = &amp; x+y\u00a0 \\\\<br \/>\n{} &amp; = &amp; 34\\cos 26{}^\\text{o}+\\frac{34\\cos 26{}^\\text{o}\\times tg\\ 26{}^\\text{o}}{tg\\ 31{}^\\text{o}}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 34\\cos 26{}^\\text{o}\\times \\frac{tg\\ 26{}^\\text{o}+tg\\ 31{}^\\text{o}}{tg\\ 31{}^\\text{o}}\u00a0 \\\\<br \/>\n{} &amp; \\simeq\u00a0 &amp; 55,4\\ (m)\u00a0 \\\\<br \/>\n\\end{array}\\]<\/p>\n<p>A dist\u00e2ncia da porta da escola \u00e0 est\u00e1tua \u00e9, aproximadamente, 55,4 metros.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_3222' onClick='GTTabs_show(0,3222)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado O Jo\u00e3o e a Maria pretendem determinar a dist\u00e2ncia da porta A da sua escola \u00e0 est\u00e1tua E. Para isso, espetaram no jardim da escola uma estaca B, a 34 metros&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20795,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,99],"tags":[422,423],"series":[],"class_list":["post-3222","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-trigonometria","tag-11-o-ano","tag-trigonometria"],"views":1726,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/09\/11V1Pag090-28_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3222","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=3222"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/3222\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20795"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3222"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3222"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3222"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=3222"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}