{"id":14262,"date":"2018-04-03T17:04:37","date_gmt":"2018-04-03T16:04:37","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=14262"},"modified":"2022-01-11T13:47:51","modified_gmt":"2022-01-11T13:47:51","slug":"a-distancia-entre-duas-arvores","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=14262","title":{"rendered":"A dist\u00e2ncia entre duas \u00e1rvores"},"content":{"rendered":"<p><ul id='GTTabs_ul_14262' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_14262' class='GTTabs_curr'><a  id=\"14262_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_14262' ><a  id=\"14262_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_14262'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14263\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14263\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19.png\" data-orig-size=\"560,420\" 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=\"\u00c1rvores\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19.png\" class=\"alignright size-medium wp-image-14263\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19-300x225.png\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19-300x225.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19.png 560w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Observa a figura ao lado.<\/p>\n<p>Calcula a dist\u00e2ncia, arredondada \u00e0s d\u00e9cimas, entre as \u00e1rvores B e C.<\/p>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_14262' onClick='GTTabs_show(1,14262)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_14262'>\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\/9V2Pag63-19.png\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"14263\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=14263\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19.png\" data-orig-size=\"560,420\" 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=\"\u00c1rvores\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19.png\" class=\"alignright size-medium wp-image-14263\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19-300x225.png\" alt=\"\" width=\"300\" height=\"225\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19-300x225.png 300w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19.png 560w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a>Seja B&#8217; a proje\u00e7\u00e3o ortogonal do ponto B sobre o segmento de reta [<em>AC<\/em>].<\/p>\n<p>No tri\u00e2ngulo ret\u00e2ngulo [<em>ABB&#8217;<\/em>], vem:<\/p>\n<p>\\[\\begin{array}{*{20}{l}}{{\\mathop{\\rm sen}\\nolimits} B\\widehat AC = \\frac{{\\overline {BB&#8217;} }}{{\\overline {AB} }}}&amp; \\Leftrightarrow &amp;{{\\mathop{\\rm sen}\\nolimits} 30^\\circ = \\frac{{\\overline {BB&#8217;} }}{{100}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\frac{1}{2} = \\frac{{\\overline {BB&#8217;} }}{{100}}}\\\\{}&amp; \\Leftrightarrow &amp;{\\overline {BB&#8217;} = 50}\\end{array}\\]<\/p>\n<p>Como o tri\u00e2ngulo [<em>BB&#8217;C<\/em>] \u00e9 ret\u00e2ngulo is\u00f3sceles, vem:<\/p>\n<p>\\[\\overline {BC} = \\sqrt 2 \\times \\overline {BB&#8217;} = 50\\sqrt 2 \\approx 70,7\\]<\/p>\n<p>Portanto, as \u00e1rvores B e C distam, aproximadamente, 70,7 metros.<\/p><\/p>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_14262' onClick='GTTabs_show(0,14262)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Observa a figura ao lado. Calcula a dist\u00e2ncia, arredondada \u00e0s d\u00e9cimas, entre as \u00e1rvores B e C. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14265,"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-14262","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":3449,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/04\/9V2Pag63-19a.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14262","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=14262"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/14262\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14265"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=14262"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=14262"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=14262"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=14262"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}