{"id":17902,"date":"2020-09-15T16:32:50","date_gmt":"2020-09-15T19:32:50","guid":{"rendered":"https:\/\/beduka.com\/blog\/?p=17902"},"modified":"2020-09-15T16:34:00","modified_gmt":"2020-09-15T19:34:00","slug":"relacoes-metricas-no-triangulo-retangulo","status":"publish","type":"post","link":"https:\/\/beduka.com\/blog\/exercicios\/matematica-exercicios\/relacoes-metricas-no-triangulo-retangulo\/","title":{"rendered":"Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo com Gabarito"},"content":{"rendered":"\n<blockquote class=\"wp-block-quote\"><p><strong><em> Rela\u00e7\u00f5es M\u00e9tricas de um Tri\u00e2ngulo Ret\u00e2ngulo s\u00e3o equa\u00e7\u00f5es capazes de relacionar as medidas dos segmentos dentro de um tri\u00e2ngulo ret\u00e2ngulo. Leia nosso resumo e coloque seu conhecimento em pr\u00e1tica com <\/em><\/strong> <strong>Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngul<em>o selecionados dos maiores vestibulares do Brasil.<\/em><\/strong><\/p><\/blockquote>\n\n\n\n<p>Quando voc\u00ea terminar os <strong>Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo<\/strong>, fa\u00e7a nosso <a href=\"https:\/\/beduka.com\/simulado-enem\/#\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Simulado Enem<\/a>. Teste seu conhecimento, escolhendo as mat\u00e9rias que deseja praticar.<\/p>\n\n\n\n<p><strong>Uma das mais importantes formas geom\u00e9tricas para a matem\u00e1tica, \u00e9 o tri\u00e2ngulo.<\/strong> Ele \u00e9 muito cobrado nos vestibulares e serve como base de compreens\u00e3o de muitas outras figuras geom\u00e9tricas.<\/p>\n\n\n\n<p>Chamamos de<strong> tri\u00e2ngulo ret\u00e2ngulo<\/strong> o tri\u00e2ngulo que <strong>possui um dos tr\u00eas \u00e2ngulos igual a 90\u00b0<\/strong>, tamb\u00e9m denominado de \u00e2ngulo reto.<\/p>\n\n\n\n<ul><li>Voc\u00ea sabe <a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/como-aprender-geometria\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">como Aprender Geometria?<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">O que s\u00e3o Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo?<\/h2>\n\n\n\n<p><strong>Rela\u00e7\u00f5es M\u00e9tricas de um Tri\u00e2ngulo Ret\u00e2ngulo s\u00e3o equa\u00e7\u00f5es capazes de relacionar as medidas dos segmentos dentro de um tri\u00e2ngulo ret\u00e2ngulo.<\/strong> Saber essas equa\u00e7\u00f5es far\u00e1 com que voc\u00ea consiga fazer exerc\u00edcios que envolvam tri\u00e2ngulo de maneira mais r\u00e1pida e precisa.<\/p>\n\n\n\n<p>Para estudarmos as rela\u00e7\u00f5es m\u00e9tricas, <strong>\u00e9 necess\u00e1rio que voc\u00ea recorde algumas caracter\u00edsticas do tri\u00e2ngulo ret\u00e2ngulo:<\/strong><\/p>\n\n\n\n<p><strong>O tri\u00e2ngulo ret\u00e2ngulo possui um \u00e2ngulo reto (90\u00b0)<\/strong>. Dois dos seus lados s\u00e3o chamados <strong>Catetos<\/strong> e o terceiro \u00e9 chamado de <strong>Hipotenusa<\/strong>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Catetos<\/h3>\n\n\n\n<p>S\u00e3o os lados que formam o \u00e2ngulo reto (90\u00b0), ou seja, s\u00e3o os lados que tocam neste \u00e2ngulo.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Hipotenusa<\/h3>\n\n\n\n<p>\u00c9 o lado que n\u00e3o toca no \u00e2ngulo de 90\u00b0. \u00c9 tamb\u00e9m o maior lado!<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-1.jpg\" alt=\"O que \u00e9 trigonometria?\" class=\"wp-image-17914\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">O que \u00e9 o teorema de Pit\u00e1goras?<\/h3>\n\n\n\n<p>O Teorema de Pit\u00e1goras \u00e9 a Primeira Rela\u00e7\u00e3o M\u00e9trica do Tri\u00e2ngulo Ret\u00e2ngulo. <strong>Ele explica a rela\u00e7\u00e3o entre os catetos e a hipotenusa.<\/strong> Representada com a seguinte f\u00f3rmula:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-2.jpg\" alt=\"Representa\u00e7\u00e3o do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17913\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-2.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-2-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-2-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Significa:<\/strong> a hipotenusa ao quadrado \u00e9 igual ao cateto adjacente ao quadrado somado ao cateto oposto ao quadrado.<\/p>\n\n\n\n<ul><li>Aprenda mais sobre Teorema de Pit\u00e1goras estudando <a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/trigonometria-no-triangulo-retangulo\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Trigonometria<\/a>.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Qual \u00e9 a Segunda Rela\u00e7\u00e3o M\u00e9trica do Tri\u00e2ngulo Ret\u00e2ngulo?<\/h3>\n\n\n\n<p><strong>A hipotenusa \u00e9 igual \u00e0 soma das proje\u00e7\u00f5es dos catetos<\/strong>, observe:<br><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-3.jpg\" alt=\"Representa\u00e7\u00e3o do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17912\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-3.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-3-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-3-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p>Chamamos de <strong>proje\u00e7\u00e3o dos catetos<\/strong> as<strong> partes representadas pela letra \u201cm\u201d e pela letra \u201cn\u201d. <\/strong>Sendo assim, podemos descrever a defini\u00e7\u00e3o dada anteriormente de maneira muito simples:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-4.jpg\" alt=\"Equa\u00e7\u00e3o do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17911\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-4.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-4-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-4-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Leia-se:<\/strong> a (hipotenusa) \u00e9 igual ao valor de m (proje\u00e7\u00e3o do cateto) mais o valor de n (proje\u00e7\u00e3o do cateto).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Qual \u00e9 a Terceira Rela\u00e7\u00e3o M\u00e9trica do Tri\u00e2ngulo Ret\u00e2ngulo?<\/h3>\n\n\n\n<p>A altura ao quadrado \u00e9 igual ao produto das proje\u00e7\u00f5es dos catetos.&nbsp;<\/p>\n\n\n\n<p>Observe que <strong>a altura do tri\u00e2ngulo est\u00e1 representada pela letra h<\/strong>, sendo assim, podemos descrever essa rela\u00e7\u00e3o com a seguinte equa\u00e7\u00e3o:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-5.jpg\" alt=\"F\u00f3rmula do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17908\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-5.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-5-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-5-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Leia-se:<\/strong> h (altura) ao quadrado \u00e9 igual a m (proje\u00e7\u00e3o do cateto) vezes n (proje\u00e7\u00e3o do cateto).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Qual \u00e9 a Quarta Rela\u00e7\u00e3o M\u00e9trica do Tri\u00e2ngulo Ret\u00e2ngulo?<\/h3>\n\n\n\n<p><strong>A quarta rela\u00e7\u00e3o<\/strong> \u00e9 utilizada para descobrir o valor dos catetos quando j\u00e1 sabemos o valor da proje\u00e7\u00e3o e o valor da hipotenusa.<\/p>\n\n\n\n<p>Para ficar mais claro, observe as f\u00f3rmulas, sempre baseando-se na seguinte imagem:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-1.jpg\" alt=\"Representa\u00e7\u00e3o do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17907\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-3-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-6.jpg\" alt=\"F\u00f3rmula do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17906\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-6.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-6-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-6-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Leia-se<\/strong>: b\u00b2&nbsp; (cateto) ao quadrado \u00e9 igual hipotenusa (a) multiplicada pela proje\u00e7\u00e3o do cateto (n)<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-7.jpg\" alt=\"F\u00f3rmula do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17905\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-7.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-7-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-7-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Leia-se<\/strong>: c\u00b2&nbsp; (cateto) ao quadrado \u00e9 igual hipotenusa (a) multiplicada pela proje\u00e7\u00e3o do cateto (m)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Qual \u00e9 a Quinta Rela\u00e7\u00e3o M\u00e9trica do Tri\u00e2ngulo Ret\u00e2ngulo?<\/h3>\n\n\n\n<p>O produto entre a hipotenusa e a altura \u00e9 sempre igual ao produto das medidas do catetos.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-8.jpg\" alt=\"F\u00f3rmula do Tri\u00e2ngulo Ret\u00e2ngulo\" class=\"wp-image-17904\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-8.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-8-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/09\/imagem-8-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Leia-se =<\/strong> hipotenusa (a) vezes a altura <strong>\u00e9 igual<\/strong> ao cateto (b) vezes o outro cateto [c].<\/p>\n\n\n\n<ul><li>Aproveite para fazer mais <a href=\"https:\/\/beduka.com\/blog\/exercicios\/matematica-exercicios\/exercicios-de-triangulos\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Exerc\u00edcios sobre Tri\u00e2ngulos<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo&nbsp;<\/h2>\n\n\n\n<p>Chegou o momento de colocar em pr\u00e1tica todo o seu conhecimento fazendo <strong>exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo.<\/strong>&nbsp;<\/p>\n\n\n\n<p><strong>Parab\u00e9ns<\/strong> por ter lido at\u00e9 aqui!!!&nbsp;<\/p>\n\n\n\n<p><strong>Baixe gratuitamente <\/strong>o <a href=\"https:\/\/beduka.com\/blog\/dicas\/enem-dicas\/plano-de-estudos-gratuito\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Plano de Estudos<\/a> do Beduka e <strong>tenha uma prepara\u00e7\u00e3o perfeita para o ENEM.<\/strong><\/p>\n\n\n\n<p><strong>Quest\u00e3o 1 &#8211;<\/strong> <a href=\"http:\/\/www2.ifsp.edu.br\/index.php\/processo-seletivo\/3972-2o-semestre-de-2015.html\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(IFSP\/2015)<\/a> O transporte alternativo \u00e9 uma maneira de locomover-se usando um meio diferente dos mais tradicionais. A bicicleta \u00e9 um exemplo disso. Em alguns lugares, ela \u00e9 usada porque \u00e9 mais barata, como no interior do Brasil e em pa\u00edses como a \u00cdndia e China. Outras pessoas escolhem andar de bicicleta por uma quest\u00e3o ideol\u00f3gica, porque elas n\u00e3o agridem o meio ambiente e n\u00e3o causam tantos transtornos quanto os carros. Usando uma bicicleta, uma pessoa sai do ponto A e dirige-se ao ponto B. O percurso, dado em km, representado pelos segmentos AC, CD e DB est\u00e1 esbo\u00e7ado no gr\u00e1fico abaixo.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/Jni1xG29Jve1Nq4ch6n9Y4ZJZON8hIvgC1wAqnzoIk8onTti3VrirMuMnCcFbhFqvqGl3NfMqJc4foPoAPs-6tP0f6vkqoNqH5iAPkmgZLVvlsIKuPMC0Jv23AtU2BSMw5Zax-hR\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Considerando <strong>\u221a2 = 1,4<\/strong> assinale a alternativa que apresenta a dist\u00e2ncia percorrida pela pessoa do ponto <strong>A <\/strong>ao ponto <strong>B<\/strong>.<\/p>\n\n\n\n<p><strong>a)<\/strong> 56 km<\/p>\n\n\n\n<p><strong>b)<\/strong> 21 km<\/p>\n\n\n\n<p><strong>c) <\/strong>20 km<\/p>\n\n\n\n<p><strong>d)<\/strong> 15 km<\/p>\n\n\n\n<p><strong>e)<\/strong> 10 km<\/p>\n\n\n\n<p><strong>Quest\u00e3o 2 &#8211;<\/strong> <a href=\"http:\/\/www.idecan.org.br\/getConc.aspx?key=7Om2oS83nco=\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(IDECAN 2016)<\/a> Um tri\u00e2ngulo ret\u00e2ngulo e possui uma hipotenusa que mede y e um de seus catetos vale x. Um \u00e2ngulo a \u00e9 marcado neste tri\u00e2ngulo, conforme mostra figura:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/nWT_Gxy-EnS4woCwztmnS-p3rMUmkkhYl6FVP_5mq-3YzNM0Hs5eVChaLQsgv3xlmhR_Vxqw3Y9-4M8-mCD7K-wJuwb7Xib-SQaDMw4siWqU1bW5Sk9Zl0h7eyGKHBLXiM8on9Fx\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/CBOgUkmfpCTLUdFP2guKe35geJ6DjOxuVcbs-IWWPU5ljc1dGrE8gEvFQo2izLAHwh8tqj-_elzQFjfKYooYAsHId63A0EK77N3ebsZMfV8Wk5J3uviyPJMgXZgIZrFqZeMwsfas\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p><strong>Sabendo que , pode-se concluir que o \u00e2ngulo a vale:<\/strong><\/p>\n\n\n\n<p><strong>a) <\/strong>15\u00b0<\/p>\n\n\n\n<p><strong>b) <\/strong>30\u00b0<\/p>\n\n\n\n<p><strong>c) <\/strong>45\u00b0<\/p>\n\n\n\n<p><strong>d) <\/strong>60\u00b0<\/p>\n\n\n\n<p><strong>Quest\u00e3o 3 &#8211;<\/strong> <a rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\" href=\"https:\/\/www.vunesp.com.br\/VNSP1611\" target=\"_blank\">(UNESP 2017)<\/a> Arthur desenhou numa folha de papel o tri\u00e2ngulo ret\u00e2ngulo a seguir. Ele afirmou, corretamente, que a medida do segmento XY a medida do segmento YZ \u00e9 igual \u00e0 medida do segmento XZ mais ________ cm.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/VF6GKq_-hypiTKt9RY5h-Tn8EmO15TNNvRfVgKx8FU4Lc4vGQhelMF-8Zc9PQxu4PPCO4Gk-qtZewyBoeSkA20oq7e_utXqZUMmmIICvZNUiUxdqSqkC534zr6PDizW2ltQF7b0v\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p>Das alternativas a seguir, aquela que completa corretamente a afirma\u00e7\u00e3o de Arthur \u00e9:<\/p>\n\n\n\n<p><strong>a) <\/strong>6<\/p>\n\n\n\n<p><strong>b) <\/strong>5<\/p>\n\n\n\n<p><strong>c) <\/strong>4<\/p>\n\n\n\n<p><strong>d) <\/strong>3<\/p>\n\n\n\n<p><strong>e) <\/strong>2<\/p>\n\n\n\n<p><strong>Quest\u00e3o 4 &#8211;<\/strong> <a href=\"https:\/\/www.ibade.org.br\/Concurso\/365\/ProvasGabaritos\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(IBADE 2018)<\/a> Considere um tri\u00e2ngulo ret\u00e2ngulo tal que o cosseno de um de seus \u00e2ngulos agudos \u00e9 igual a 0,8. Sabendo-se que a hipotenusa desse ret\u00e2ngulo \u00e9 igual a 4, o valor da tangente deste mesmo \u00e2ngulo \u00e9:<\/p>\n\n\n\n<p><strong>a) <\/strong>0,75<\/p>\n\n\n\n<p><strong>b) <\/strong>1<\/p>\n\n\n\n<p><strong>c) <\/strong>0,7<\/p>\n\n\n\n<p><strong>d) <\/strong>0,5<\/p>\n\n\n\n<p><strong>Quest\u00e3o 5 &#8211;<\/strong> <a href=\"http:\/\/ufrr.br\/cpv\/index.php?option=com_phocadownload&amp;view=category&amp;id=67:vestibular-2015\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">(UFRR 2015)<\/a> Sobre os lados do tri\u00e2ngulo ret\u00e2ngulo ABC, foram desenhados pent\u00e1gonos regulares cujas \u00e1reas s\u00e3o S1 ,S2 e S3 , conforme indica a figura abaixo. Sabendo-se que 2 3 os lados AB e AC t\u00eam o mesmo comprimento, \u00e9 correto afirmar que:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/zkc_RCKUx959MTd9wt2hIPwteTa5ItxFLNwxU5I5Ky4rUEsqBtTK0TgDuF6MRVmUQtKpy1k-r-elZCwiAVCC7Rr3PYQrVTP1Lilz0RLKL1JFUtPthk0ErwGs4YeFTueZbtV0zQSt\" alt=\"\"\/><\/figure><\/div>\n\n\n\n<p><strong>a)<\/strong> S1 &lt; S2 &lt; S3<\/p>\n\n\n\n<p><strong>b) <\/strong>S1\u00b2 = S2\u00b2 + S3\u00b3<\/p>\n\n\n\n<p><strong>c) <\/strong>S1 &gt; S2 + S3<\/p>\n\n\n\n<p><strong>d) <\/strong>S1 = S2 + S3<\/p>\n\n\n\n<p><strong>e) <\/strong>S2 = S1 \/ S3<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Respostas dos exerc\u00edcios de Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo<\/h2>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 1 &#8211;<\/strong><br><\/p>\n\n\n\n<p>Alternativa correta: a) 56 km<br><\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 2 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>b) 30\u00b0<\/strong><\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 3 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>a)<\/strong> 6<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 4 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>a) <\/strong>0,75<\/p>\n\n\n\n<p><strong>Exerc\u00edcio resolvido da quest\u00e3o 5 &#8211;<\/strong><\/p>\n\n\n\n<p>Alternativa correta: <strong>&nbsp;<\/strong><strong>d) <\/strong>S1 = S2 + S3<\/p>\n\n\n\n<p>Estude para o Enem com o <a href=\"https:\/\/beduka.com\/simulado\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Simulado Beduka.<\/a> <strong>\u00c9 gratuito!<\/strong><\/p>\n\n\n\n<p>Gostou dos nossos <strong>Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo?<\/strong> Compartilhe com os seus amigos e comente abaixo sobre as \u00e1reas que voc\u00ea deseja mais explica\u00e7\u00f5es.<\/p>\n\n\n\n<p>Queremos te ajudar a encontrar a <strong>FACULDADE IDEAL! <\/strong>Logo abaixo, fa\u00e7a uma pesquisa por curso e cidade que te mostraremos todas as faculdades que podem te atender. <strong>Informamos a nota de corte, valor de mensalidade, nota do MEC, avalia\u00e7\u00e3o dos alunos, modalidades de ensino e muito mais.<\/strong><br><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Rela\u00e7\u00f5es M\u00e9tricas de um Tri\u00e2ngulo Ret\u00e2ngulo s\u00e3o equa\u00e7\u00f5es capazes de relacionar as medidas dos segmentos dentro de um tri\u00e2ngulo ret\u00e2ngulo. Leia nosso resumo e coloque seu conhecimento em pr\u00e1tica com Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo selecionados dos maiores vestibulares do Brasil. Quando voc\u00ea terminar os Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo, fa\u00e7a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":17915,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[610],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.10 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo com Gabarito<\/title>\n<meta name=\"description\" content=\"Coloque seu conhecimento em pr\u00e1tica com Exerc\u00edcios de Rela\u00e7\u00f5es M\u00e9tricas no Tri\u00e2ngulo Ret\u00e2ngulo selecionados dos maiores vestibulares do Brasil.\" \/>\n<meta name=\"robots\" content=\"index, follow, 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