{"id":6127,"date":"2026-10-21T08:08:25","date_gmt":"2026-10-21T05:08:25","guid":{"rendered":"https:\/\/wpcalc.com\/fr\/mathematiques\/calculateur-triangle-rectangle\/"},"modified":"2026-10-21T08:08:25","modified_gmt":"2026-10-21T05:08:25","slug":"calculateur-triangle-rectangle","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/fr\/mathematiques\/calculateur-triangle-rectangle\/","title":{"rendered":"Calculateur de triangle rectangle"},"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\">R\u00e9soudre un triangle rectangle \u00e0 partir de deux mesures<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"6127\" data-favorite-title=\"Triangle rectangle\" data-favorite-url=\"https:\/\/wpcalc.com\/fr\/mathematiques\/calculateur-triangle-rectangle\/\" data-favorite-excerpt=\"R\u00e9solvez un triangle rectangle \u00e0 partir de deux mesures connues, dont au moins un c\u00f4t\u00e9. Saisissez des longueurs de c\u00f4t\u00e9s, un angle aigu, une aire ou un p\u00e9rim\u00e8tre pour obtenir les mesures restantes.\" aria-label=\"Ajouter aux favoris\" 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\/fr\/mathematiques\/calculateur-triangle-rectangle\/\" method=\"POST\" class=\"calculator\" id=\"calculator-6127\" data-post=\"6127\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Champs de saisie<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">C\u00f4t\u00e9 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=\"ct_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\">Oppos\u00e9 \u00e0 l\u2019angle \u03b1. Saisissez les longueurs dans la m\u00eame unit\u00e9.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">C\u00f4t\u00e9 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=\"ct_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\">Oppos\u00e9 \u00e0 l\u2019angle \u03b2.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Hypot\u00e9nuse 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=\"hypotnuse_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\">Angle \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=\"angle_\" 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\">Angle oppos\u00e9 au c\u00f4t\u00e9 a\u00a0; il doit \u00eatre compris entre 0\u00b0 et 90\u00b0.<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Angle \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=\"angle_\" 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\">Angle oppos\u00e9 au c\u00f4t\u00e9 b\u00a0; il doit \u00eatre compris entre 0\u00b0 et 90\u00b0.<\/small><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-6\">Aire<\/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=\"aire\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\"\/><small id=\"calc-info-6\">Valeur connue facultative, en unit\u00e9s carr\u00e9es.<\/small><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-7\">P\u00e9rim\u00e8tre<\/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=\"primtre\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\"\/><small id=\"calc-info-7\">Valeur connue facultative, dans la m\u00eame unit\u00e9 de longueur que les c\u00f4t\u00e9s.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalculer\" id=\"calculate-button\" data-post=\"6127\">Calculer<\/button><button type=\"reset\">R\u00e9initialiser<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculer automatiquement<\/label><small>Si activ\u00e9, le r\u00e9sultat se met \u00e0 jour automatiquement d\u00e8s que vous modifiez une valeur.<\/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> Triangle r\u00e9solu<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>C\u00f4t\u00e9 a<\/span><span class=\"result-term\">a<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"unit\u00e9s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>C\u00f4t\u00e9 b<\/span><span class=\"result-term\">b<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"unit\u00e9s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Hypot\u00e9nuse c<\/span><span class=\"result-term\">c<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"unit\u00e9s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Angle \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=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Angle \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=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Angle \u03b1 en radians<\/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=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Angle \u03b2 en radians<\/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=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Aire<\/span><span class=\"result-term\">A<\/span><\/span><span class=\"field-value\" id=\"result-8\" data-unit=\"unit\u00e9s\u00b2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>P\u00e9rim\u00e8tre<\/span><span class=\"result-term\">P<\/span><\/span><span class=\"field-value\" id=\"result-9\" data-unit=\"unit\u00e9s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Hauteur relative \u00e0 l\u2019hypot\u00e9nuse<\/span><span class=\"result-term\">h<\/span><\/span><span class=\"field-value\" id=\"result-10\" data-unit=\"unit\u00e9s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Rayon du cercle inscrit<\/span><span class=\"result-term\">r<\/span><\/span><span class=\"field-value\" id=\"result-11\" data-unit=\"unit\u00e9s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Rayon du cercle circonscrit<\/span><span class=\"result-term\">R<\/span><\/span><span class=\"field-value\" id=\"result-12\" data-unit=\"unit\u00e9s\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Mesures utilis\u00e9es<\/span><\/span><span class=\"field-value\" id=\"result-13\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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>Triangle \u00e0 l\u2019\u00e9chelle<\/span><\/span><span class=\"field-value\" id=\"result-14\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><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\">Copier le lien vers ce calcul<\/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>Laisser un commentaire<\/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=\"6127\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Que pensez-vous de ce r\u00e9sultat\u00a0?<\/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\">J\u2019aime <\/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\">Utile <\/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\">Confus <\/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\">D\u00e9\u00e7u <\/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\">Inexact <\/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>Formules du triangle rectangle<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formule<\/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>Avec :<\/strong><\/p>\n<ul>\n<li>\\(a\\) et \\(b\\) \u2014 les c\u00f4t\u00e9s de l'angle droit, oppos\u00e9s respectivement aux angles \\(\\alpha\\) et \\(\\beta\\)<\/li>\n<li>\\(c\\) \u2014 l'hypot\u00e9nuse, oppos\u00e9e \u00e0 l'angle droit<\/li>\n<li>\\(A\\) \u2014 l'aire ; \\(P\\) \u2014 le p\u00e9rim\u00e8tre<\/li>\n<li>\\(h\\) \u2014 la hauteur issue du sommet de l'angle droit sur l'hypot\u00e9nuse<\/li>\n<li>\\(r\\) \u2014 le rayon du cercle inscrit ; \\(R\\) \u2014 le rayon du cercle circonscrit<\/li>\n<\/ul>\n<p>Le th\u00e9or\u00e8me de Pythagore et la trigonom\u00e9trie permettent de d\u00e9terminer les c\u00f4t\u00e9s et les angles aigus. Une fois le triangle r\u00e9solu, ses c\u00f4t\u00e9s d\u00e9terminent \u00e9galement son aire, son p\u00e9rim\u00e8tre, sa hauteur et les rayons des cercles inscrit et circonscrit.<\/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>Triangle rectangle \u2013 Exemple de calcul<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemple :<\/strong> les valeurs par d\u00e9faut sont C\u00f4t\u00e9 a = 3 et C\u00f4t\u00e9 b = 4. Trouvez les mesures restantes.<\/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>R\u00e9sultat :<\/strong> les c\u00f4t\u00e9s mesurent 3, 4 et 5 unit\u00e9s ; les angles aigus valent environ 36,8699\u00b0 et 53,1301\u00b0. L'aire est de 6 unit\u00e9s carr\u00e9es et le p\u00e9rim\u00e8tre de 12 unit\u00e9s.<\/p>\n<p>\n\r\n<\/section>\n<h2>Comment utiliser le calculateur<\/h2>\n<ol>\n<li>Saisissez deux mesures connues, dont au moins un c\u00f4t\u00e9. Les champs de c\u00f4t\u00e9s sont <strong>C\u00f4t\u00e9 a<\/strong>, <strong>C\u00f4t\u00e9 b<\/strong> et <strong>Hypot\u00e9nuse c<\/strong>. Le c\u00f4t\u00e9 a est oppos\u00e9 \u00e0 l'angle \u03b1 ; le c\u00f4t\u00e9 b est oppos\u00e9 \u00e0 l'angle \u03b2.<\/li>\n<li>Pour un calcul \u00e0 partir d'un c\u00f4t\u00e9 et d'un angle, saisissez un c\u00f4t\u00e9 ainsi que l'<strong>Angle \u03b1<\/strong> ou l'<strong>Angle \u03b2<\/strong> en degr\u00e9s. Vous pouvez aussi associer un c\u00f4t\u00e9 \u00e0 l'<strong>Aire<\/strong> ou au <strong>P\u00e9rim\u00e8tre<\/strong>. Saisissez toutes les longueurs dans la m\u00eame unit\u00e9 et l'aire dans l'unit\u00e9 carr\u00e9e correspondante.<\/li>\n<li>Effacez les valeurs par d\u00e9faut des champs <strong>C\u00f4t\u00e9 a<\/strong> et <strong>C\u00f4t\u00e9 b<\/strong> si elles ne font pas partie de vos mesures connues. Laissez vides les champs que vous ne souhaitez pas utiliser.<\/li>\n<li>Consultez <strong>Triangle r\u00e9solu<\/strong> pour obtenir les c\u00f4t\u00e9s, les angles en degr\u00e9s et en radians, l'aire, le p\u00e9rim\u00e8tre, la hauteur relative \u00e0 l'hypot\u00e9nuse, le rayon du cercle inscrit et le rayon du cercle circonscrit. V\u00e9rifiez <strong>Mesures utilis\u00e9es<\/strong> pour savoir quelles donn\u00e9es ont d\u00e9termin\u00e9 le r\u00e9sultat.<\/li>\n<\/ol>\n<h2>Ce que vous apprend le triangle r\u00e9solu<\/h2>\n<p>Un triangle rectangle comporte un angle de 90\u00b0. Ses deux c\u00f4t\u00e9s de l'angle droit se rejoignent en ce sommet, et l'hypot\u00e9nuse est le c\u00f4t\u00e9 qui lui est oppos\u00e9. Les angles aigus \u03b1 et \u03b2 sont compl\u00e9mentaires : leur somme vaut 90\u00b0. Conna\u00eetre deux mesures adapt\u00e9es, dont au moins un c\u00f4t\u00e9, d\u00e9termine g\u00e9n\u00e9ralement \u00e0 la fois la forme et la taille du triangle. Deux angles seuls fixent la forme, mais pas les longueurs des c\u00f4t\u00e9s.<\/p>\n<p>L'hypot\u00e9nuse se calcule \u00e0 partir des deux c\u00f4t\u00e9s de l'angle droit gr\u00e2ce \u00e0 \\(a^2+b^2=c^2\\). Si un c\u00f4t\u00e9 et un angle aigu sont connus, les rapports trigonom\u00e9triques les relient aux autres c\u00f4t\u00e9s. Par exemple, \\(\\tan\\alpha=a\/b\\) et \\(\\sin\\alpha=a\/c\\). Pour un calcul cibl\u00e9 utilisant ces relations, consultez le <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/theoreme-de-pythagore\/\">Calculateur de th\u00e9or\u00e8me de Pythagore<\/a> ou le <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/trigonometry-calculator\/\">Calculateur de trigonom\u00e9trie<\/a>.<\/p>\n<p>L'aire vaut la moiti\u00e9 du produit des c\u00f4t\u00e9s de l'angle droit, car ils servent de base et de hauteur perpendiculaires. La <strong>Hauteur relative \u00e0 l'hypot\u00e9nuse<\/strong> affich\u00e9e est une autre hauteur : elle part du sommet de l'angle droit et rejoint l'hypot\u00e9nuse. Le rayon du cercle inscrit est celui du cercle tangent aux trois c\u00f4t\u00e9s ; le rayon du cercle circonscrit est celui du cercle passant par les trois sommets. Dans un triangle rectangle, le rayon du cercle circonscrit est toujours \u00e9gal \u00e0 la moiti\u00e9 de l'hypot\u00e9nuse. Si vous cherchez simplement l'aire \u00e0 partir d'autres mesures d'un triangle, utilisez le <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/triangle-area-calculator\/\">Calculateur d'aire d'un triangle<\/a>.<\/p>\n<h2>R\u00e8gles de saisie et limites pratiques<\/h2>\n<p>Saisissez des mesures positives et finies. Chaque angle aigu doit \u00eatre strictement sup\u00e9rieur \u00e0 0\u00b0 et inf\u00e9rieur \u00e0 90\u00b0, et l'hypot\u00e9nuse doit \u00eatre plus longue que chaque c\u00f4t\u00e9 connu. Un c\u00f4t\u00e9 associ\u00e9 \u00e0 une aire ou \u00e0 un p\u00e9rim\u00e8tre doit \u00e9galement correspondre \u00e0 un triangle rectangle possible ; le calculateur signale une erreur dans le cas contraire.<\/p>\n<p>Le calculateur n'utilise que deux valeurs saisies. Il retient les deux premiers c\u00f4t\u00e9s disponibles dans l'ordre C\u00f4t\u00e9 a, C\u00f4t\u00e9 b, Hypot\u00e9nuse c. Si un seul c\u00f4t\u00e9 est saisi, il l'associe \u00e0 la premi\u00e8re valeur disponible dans cet ordre : Angle \u03b1, Angle \u03b2, Aire, P\u00e9rim\u00e8tre. Les autres saisies sont ignor\u00e9es plut\u00f4t que v\u00e9rifi\u00e9es pour coh\u00e9rence : effacez donc les champs inutiles et consultez <strong>Mesures utilis\u00e9es<\/strong>.<\/p>\n<p>Une hypot\u00e9nuse associ\u00e9e \u00e0 une aire ou \u00e0 un p\u00e9rim\u00e8tre peut autoriser deux \u00e9tiquetages de la m\u00eame forme : \u00e9changer les c\u00f4t\u00e9s a et b \u00e9change aussi les angles \u03b1 et \u03b2. Le r\u00e9sultat et le sch\u00e9ma, mis \u00e0 l'\u00e9chelle, affichent l'\u00e9tiquetage avec \\(a\\leq b\\) ; une note sous <strong>Mesures utilis\u00e9es<\/strong> signale le cas o\u00f9 l'\u00e9tiquetage invers\u00e9 est \u00e9galement possible. Le sch\u00e9ma est mis \u00e0 l'\u00e9chelle pour montrer les proportions, pas pour fournir une mesure physique \u00e0 la taille de l'\u00e9cran.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>R\u00e9solvez un triangle rectangle \u00e0 partir de deux mesures connues, dont au moins un c\u00f4t\u00e9. Saisissez des longueurs de c\u00f4t\u00e9s, un angle aigu, une aire ou un p\u00e9rim\u00e8tre pour obtenir les mesures restantes.<\/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":[2],"tags":[3],"class_list":["post-6127","post","type-post","status-publish","format-standard","hentry","category-mathematiques","tag-geometrie"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/6127","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/comments?post=6127"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/6127\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/media?parent=6127"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/categories?post=6127"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/tags?post=6127"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}