{"id":2971,"date":"2026-10-20T14:12:39","date_gmt":"2026-10-20T13:12:39","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-triangulo-retangulo\/"},"modified":"2026-10-20T14:12:39","modified_gmt":"2026-10-20T13:12:39","slug":"calculadora-triangulo-retangulo","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-triangulo-retangulo\/","title":{"rendered":"Calculadora de Tri\u00e2ngulo Ret\u00e2ngulo"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Resolva um tri\u00e2ngulo ret\u00e2ngulo a partir de duas medidas<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2971\" data-favorite-title=\"Tri\u00e2ngulo Ret\u00e2ngulo\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-triangulo-retangulo\/\" data-favorite-excerpt=\"Resolva um tri\u00e2ngulo ret\u00e2ngulo a partir de duas medidas conhecidas, incluindo pelo menos um lado. Informe os comprimentos dos lados, um \u00e2ngulo agudo, a \u00e1rea ou o per\u00edmetro para encontrar as demais medidas.\" aria-label=\"Adicionar aos favoritos\" data-favorite-icon=\"icon icon-geometry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-triangulo-retangulo\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2971\" data-post=\"2971\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Cateto a<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"cateto_a\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"3\"\/><small id=\"calc-info-1\">\u00c2ngulo oposto ao cateto a. Informe os comprimentos na mesma unidade.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Cateto b<\/label><div class=\"term\">b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"cateto_b\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"4\"\/><small id=\"calc-info-2\">\u00c2ngulo oposto ao cateto b.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Hipotenusa c<\/label><div class=\"term\">c<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"hipotenusa_c\" id=\"field-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\"\/><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">\u00c2ngulo \u03b1<\/label><div class=\"term\">\u03b1<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"ngulo_\" id=\"field-4\" aria-describedby=\"calc-unit-4 calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" max=\"90\"\/><div class=\"unit\" id=\"calc-unit-4\">\u00b0<\/div><small id=\"calc-info-4\">\u00c2ngulo oposto ao cateto a; deve estar entre 0\u00b0 e 90\u00b0.<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">\u00c2ngulo \u03b2<\/label><div class=\"term\">\u03b2<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"ngulo_\" id=\"field-5\" aria-describedby=\"calc-unit-5 calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" max=\"90\"\/><div class=\"unit\" id=\"calc-unit-5\">\u00b0<\/div><small id=\"calc-info-5\">\u00c2ngulo oposto ao cateto b; deve estar entre 0\u00b0 e 90\u00b0.<\/small><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-6\">\u00c1rea<\/label><div class=\"term\">A<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"rea\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\"\/><small id=\"calc-info-6\">Valor conhecido opcional, em unidades quadradas.<\/small><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-7\">Per\u00edmetro<\/label><div class=\"term\">P<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"permetro\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\"\/><small id=\"calc-info-7\">Valor conhecido opcional, na mesma unidade de comprimento dos lados.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2971\">Calcular<\/button><button type=\"reset\">Redefinir<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calcular automaticamente<\/label><small>Se ativado, o resultado \u00e9 atualizado automaticamente quando voc\u00ea altera qualquer valor.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Tri\u00e2ngulo resolvido<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Cateto a<\/span><span class=\"result-term\">a<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"units\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Cateto b<\/span><span class=\"result-term\">b<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"unidades\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Hipotenusa c<\/span><span class=\"result-term\">c<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"unidades\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-4\"><span class=\"field-title\"><span>\u00c2ngulo \u03b1<\/span><span class=\"result-term\">\u03b1<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"\u00b0\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-5\"><span class=\"field-title\"><span>\u00c2ngulo \u03b2<\/span><span class=\"result-term\">\u03b2<\/span><\/span><span class=\"field-value\" id=\"result-5\" data-unit=\"\u00b0\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-6\"><span class=\"field-title\"><span>\u00c2ngulo \u03b1 em radianos<\/span><span class=\"result-term\">\u03b1<\/span><\/span><span class=\"field-value\" id=\"result-6\" data-unit=\"rad\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-7\"><span class=\"field-title\"><span>\u00c2ngulo \u03b2 em radianos<\/span><span class=\"result-term\">\u03b2<\/span><\/span><span class=\"field-value\" id=\"result-7\" data-unit=\"rad\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-8\"><span class=\"field-title\"><span>\u00c1rea<\/span><span class=\"result-term\">A<\/span><\/span><span class=\"field-value\" id=\"result-8\" data-unit=\"unidades\u00b2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-9\"><span class=\"field-title\"><span>Per\u00edmetro<\/span><span class=\"result-term\">P<\/span><\/span><span class=\"field-value\" id=\"result-9\" data-unit=\"unidades\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-10\"><span class=\"field-title\"><span>Altura relativa \u00e0 hipotenusa<\/span><span class=\"result-term\">h<\/span><\/span><span class=\"field-value\" id=\"result-10\" data-unit=\"unidades\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-11\"><span class=\"field-title\"><span>Raio inscrito<\/span><span class=\"result-term\">r<\/span><\/span><span class=\"field-value\" id=\"result-11\" data-unit=\"unidades\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-12\"><span class=\"field-title\"><span>Raio circunscrito<\/span><span class=\"result-term\">R<\/span><\/span><span class=\"field-value\" id=\"result-12\" data-unit=\"unidades\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-13\"><span class=\"field-title\"><span>Medidas usadas<\/span><\/span><span class=\"field-value\" id=\"result-13\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-14\"><span class=\"field-title\"><span>Tri\u00e2ngulo em escala<\/span><\/span><span class=\"field-value\" id=\"result-14\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copiar link para este c\u00e1lculo<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Deixar um coment\u00e1rio<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"2971\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">O que voc\u00ea achou deste resultado?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Curti <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">\u00datil <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confuso <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Decepcionado <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Impreciso <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>F\u00f3rmula do tri\u00e2ngulo ret\u00e2ngulo<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">F\u00f3rmula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[\\begin{aligned}c&amp;=\\sqrt{a^2+b^2}, &amp; A&amp;=\\frac{ab}{2}, &amp; P&amp;=a+b+c\\\\ \\alpha&amp;=\\arctan\\!\\left(\\frac{a}{b}\\right), &amp; \\beta&amp;=90^\\circ-\\alpha\\\\ h&amp;=\\frac{ab}{c}, &amp; r&amp;=\\frac{ab}{P}, &amp; R&amp;=\\frac{c}{2}\\end{aligned}\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(a\\) e \\(b\\) \u2014 os catetos, opostos aos \u00e2ngulos \\(\\alpha\\) e \\(\\beta\\), respectivamente<\/li>\n<li>\\(c\\) \u2014 a hipotenusa, oposta ao \u00e2ngulo reto<\/li>\n<li>\\(A\\) \u2014 \u00e1rea; \\(P\\) \u2014 per\u00edmetro<\/li>\n<li>\\(h\\) \u2014 altura relativa \u00e0 hipotenusa, lan\u00e7ada a partir do v\u00e9rtice do \u00e2ngulo reto<\/li>\n<li>\\(r\\) \u2014 raio do c\u00edrculo inscrito; \\(R\\) \u2014 raio do c\u00edrculo circunscrito<\/li>\n<\/ul>\n<p>As medidas dos lados e dos \u00e2ngulos agudos s\u00e3o determinadas pelo teorema de Pit\u00e1goras e pela trigonometria. Uma vez resolvido o tri\u00e2ngulo, seus lados tamb\u00e9m determinam a \u00e1rea, o per\u00edmetro, a altura e os raios das circunfer\u00eancias inscrita e circunscrita.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Tri\u00e2ngulo ret\u00e2ngulo \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> os valores padr\u00e3o s\u00e3o Cateto a = 3 e Cateto b = 4. Encontre as demais medidas.<\/p>\n<p>\\[c=\\sqrt{3^2+4^2}=5,\\qquad \\alpha=\\arctan\\!\\left(\\frac{3}{4}\\right)\\approx36.8699^\\circ,\\qquad \\beta\\approx53.1301^\\circ\\]<\/p>\n<p>\\[A=\\frac{3\\cdot4}{2}=6,\\qquad P=3+4+5=12\\]<\/p>\n<p>\\[h=\\frac{3\\cdot4}{5}=2.4,\\qquad r=\\frac{3\\cdot4}{12}=1,\\qquad R=\\frac{5}{2}=2.5\\]<\/p>\n<p><strong>Resultado:<\/strong> os lados medem 3, 4 e 5 unidades; os \u00e2ngulos agudos s\u00e3o de aproximadamente 36,8699\u00b0 e 53,1301\u00b0. A \u00e1rea \u00e9 de 6 unidades quadradas e o per\u00edmetro, de 12 unidades.<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Informe duas medidas conhecidas, incluindo pelo menos um lado. Os campos de lados s\u00e3o <strong>Cateto a<\/strong>, <strong>Cateto b<\/strong> e <strong>Hipotenusa c<\/strong>. O cateto a \u00e9 oposto ao \u00e2ngulo \u03b1; o cateto b, ao \u00e2ngulo \u03b2.<\/li>\n<li>Para calcular com um lado e um \u00e2ngulo, informe um lado e o <strong>\u00c2ngulo \u03b1<\/strong> ou o <strong>\u00c2ngulo \u03b2<\/strong> em graus. Outra op\u00e7\u00e3o \u00e9 combinar um lado com a <strong>\u00c1rea<\/strong> ou o <strong>Per\u00edmetro<\/strong>. Informe todos os comprimentos na mesma unidade e a \u00e1rea na unidade quadrada correspondente.<\/li>\n<li>Apague os valores padr\u00e3o em <strong>Cateto a<\/strong> e <strong>Cateto b<\/strong> se n\u00e3o fizerem parte das medidas que voc\u00ea conhece. Deixe em branco os campos que n\u00e3o quiser usar.<\/li>\n<li>Consulte <strong>Tri\u00e2ngulo resolvido<\/strong> para ver os lados, os \u00e2ngulos em graus e radianos, a \u00e1rea, o per\u00edmetro, a altura relativa \u00e0 hipotenusa e os raios dos c\u00edrculos inscrito e circunscrito. Veja em <strong>Medidas utilizadas<\/strong> quais dados de entrada determinaram o resultado.<\/li>\n<\/ol>\n<h2>O que o tri\u00e2ngulo resolvido mostra<\/h2>\n<p>Um tri\u00e2ngulo ret\u00e2ngulo tem um \u00e2ngulo de 90\u00b0. Os dois catetos se encontram nesse \u00e2ngulo, e a hipotenusa \u00e9 o lado oposto a ele. Os \u00e2ngulos agudos \u03b1 e \u03b2 somam 90\u00b0. Conhecendo-se duas medidas adequadas, das quais pelo menos uma seja um lado, geralmente ficam determinados tanto a forma quanto o tamanho do tri\u00e2ngulo. Dois \u00e2ngulos sozinhos definem a forma, mas n\u00e3o permitem calcular os comprimentos dos lados.<\/p>\n<p>A hipotenusa pode ser encontrada a partir dos dois catetos com \\(a^2+b^2=c^2\\). Se um cateto e um \u00e2ngulo agudo s\u00e3o conhecidos, as raz\u00f5es trigonom\u00e9tricas os relacionam aos demais lados. Por exemplo, \\(\\tan\\alpha=a\/b\\) e \\(\\sin\\alpha=a\/c\\). Para um c\u00e1lculo focado nessas rela\u00e7\u00f5es, consulte a <a href=\"https:\/\/wpcalc.com\/pt\/matematica\/calculadora-teorema-de-pitagoras\/\">Calculadora de Teorema de Pit\u00e1goras<\/a> ou a <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/trigonometry-calculator\/\">Calculadora de Trigonometria<\/a>.<\/p>\n<p>A \u00e1rea \u00e9 metade do produto dos catetos, pois eles funcionam como base e altura perpendiculares entre si. J\u00e1 a <strong>altura relativa \u00e0 hipotenusa<\/strong> \u00e9 uma altura diferente: ela vai do v\u00e9rtice do \u00e2ngulo reto at\u00e9 a hipotenusa. O raio do c\u00edrculo inscrito \u00e9 o raio da circunfer\u00eancia que tangencia os tr\u00eas lados; o raio do c\u00edrculo circunscrito \u00e9 o da circunfer\u00eancia que passa pelos tr\u00eas v\u00e9rtices. Em um tri\u00e2ngulo ret\u00e2ngulo, o raio do c\u00edrculo circunscrito \u00e9 sempre a metade da hipotenusa. Se voc\u00ea precisar apenas da \u00e1rea a partir de outro conjunto de medidas, use a <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/triangle-area-calculator\/\">Calculadora de \u00c1rea de Tri\u00e2ngulo<\/a>.<\/p>\n<h2>Regras de entrada e limites pr\u00e1ticos<\/h2>\n<p>Informe medidas positivas e finitas. Cada \u00e2ngulo agudo deve ser maior que 0\u00b0 e menor que 90\u00b0, e a hipotenusa deve ser mais longa que qualquer cateto conhecido. Um lado combinado com a \u00e1rea ou o per\u00edmetro tamb\u00e9m precisa corresponder a um tri\u00e2ngulo ret\u00e2ngulo poss\u00edvel; quando n\u00e3o corresponde, a calculadora exibe um erro.<\/p>\n<p>A calculadora usa apenas dois valores informados. Ela considera os dois primeiros lados dispon\u00edveis na ordem Cateto a, Cateto b, Hipotenusa c. Se apenas um lado for informado, ele \u00e9 combinado com o primeiro valor dispon\u00edvel nesta ordem: \u00c2ngulo \u03b1, \u00c2ngulo \u03b2, \u00c1rea, Per\u00edmetro. Os demais campos s\u00e3o ignorados, e n\u00e3o h\u00e1 verifica\u00e7\u00e3o de consist\u00eancia entre eles, portanto limpe os campos que n\u00e3o quiser usar e confira <strong>Medidas utilizadas<\/strong>.<\/p>\n<p>Uma hipotenusa combinada com a \u00e1rea ou o per\u00edmetro pode admitir duas nomea\u00e7\u00f5es da mesma figura: trocando os catetos a e b, trocam-se tamb\u00e9m os \u00e2ngulos \u03b1 e \u03b2. O resultado e o desenho em escala mostram a nomea\u00e7\u00e3o com \\(a\\leq b\\); uma observa\u00e7\u00e3o em <strong>Medidas utilizadas<\/strong> indica quando a nomea\u00e7\u00e3o trocada tamb\u00e9m \u00e9 poss\u00edvel. O desenho est\u00e1 em escala para mostrar as propor\u00e7\u00f5es, n\u00e3o para servir de medida f\u00edsica no tamanho da tela.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Resolva um tri\u00e2ngulo ret\u00e2ngulo a partir de duas medidas conhecidas, incluindo pelo menos um lado. Informe os comprimentos dos lados, um \u00e2ngulo agudo, a \u00e1rea ou o per\u00edmetro para encontrar as demais medidas.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[8],"tags":[42],"class_list":["post-2971","post","type-post","status-publish","format-standard","hentry","category-matematica","tag-geometria"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2971","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/comments?post=2971"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2971\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2971"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2971"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2971"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}