{"id":67162,"date":"2026-10-20T09:51:51","date_gmt":"2026-10-20T06:51:51","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=67162"},"modified":"2026-10-20T09:51:51","modified_gmt":"2026-10-20T06:51:51","slug":"right-triangle-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/right-triangle-calculator\/","title":{"rendered":"Right Triangle Calculator"},"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\">Solve a Right Triangle from Two Measurements<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"67162\" data-favorite-title=\"Right Triangle\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/right-triangle-calculator\/\" data-favorite-excerpt=\"Solve a right triangle from two known measurements, including at least one side. Enter side lengths, an acute angle, area, or perimeter to find the remaining measurements.\" aria-label=\"Add to Favorites\" 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\/en\/mathematics\/right-triangle-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-67162\" data-post=\"67162\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Leg 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=\"leg_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\">Opposite angle \u03b1. Enter lengths in the same unit.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Leg 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=\"leg_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\">Opposite angle \u03b2.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Hypotenuse 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=\"hypotenuse_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 opposite leg a; must be between 0\u00b0 and 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 opposite leg b; must be between 0\u00b0 and 90\u00b0.<\/small><\/div><div class=\"field has-term\" id=\"input-6\"><label for=\"field-6\">Area<\/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=\"area\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\"\/><small id=\"calc-info-6\">Optional known value, in square units.<\/small><\/div><div class=\"field has-term\" id=\"input-7\"><label for=\"field-7\">Perimeter<\/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=\"perimeter\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\"\/><small id=\"calc-info-7\">Optional known value, in the same length unit as the sides.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"67162\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/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> Solved Triangle<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Leg 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=\"Copy Result\" aria-label=\"Copy Result\"><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>Leg b<\/span><span class=\"result-term\">b<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"units\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Hypotenuse c<\/span><span class=\"result-term\">c<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"units\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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=\"Copy Result\" aria-label=\"Copy Result\"><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=\"Copy Result\" aria-label=\"Copy Result\"><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 in 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=\"Copy Result\" aria-label=\"Copy Result\"><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 in 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=\"Copy Result\" aria-label=\"Copy Result\"><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>Area<\/span><span class=\"result-term\">A<\/span><\/span><span class=\"field-value\" id=\"result-8\" data-unit=\"units\u00b2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Perimeter<\/span><span class=\"result-term\">P<\/span><\/span><span class=\"field-value\" id=\"result-9\" data-unit=\"units\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Height to hypotenuse<\/span><span class=\"result-term\">h<\/span><\/span><span class=\"field-value\" id=\"result-10\" data-unit=\"units\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Inradius<\/span><span class=\"result-term\">r<\/span><\/span><span class=\"field-value\" id=\"result-11\" data-unit=\"units\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Circumradius<\/span><span class=\"result-term\">R<\/span><\/span><span class=\"field-value\" id=\"result-12\" data-unit=\"units\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Measurements used<\/span><\/span><span class=\"field-value\" id=\"result-13\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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>Scaled triangle<\/span><\/span><span class=\"field-value\" id=\"result-14\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><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\">Copy link to this calculation<\/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>Leave a Comment<\/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=\"67162\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/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\">Like <\/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\">Helpful <\/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\">Confused <\/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\">Disappointed <\/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\">Inaccurate <\/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>Right Triangle Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/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>Where:<\/strong><\/p>\n<ul>\n<li>\\(a\\) and \\(b\\) \u2014 the perpendicular legs, opposite angles \\(\\alpha\\) and \\(\\beta\\), respectively<\/li>\n<li>\\(c\\) \u2014 the hypotenuse, opposite the right angle<\/li>\n<li>\\(A\\) \u2014 area; \\(P\\) \u2014 perimeter<\/li>\n<li>\\(h\\) \u2014 height from the right-angle vertex to the hypotenuse<\/li>\n<li>\\(r\\) \u2014 inradius; \\(R\\) \u2014 circumradius<\/li>\n<\/ul>\n<p>The Pythagorean theorem and trigonometry determine the sides and acute angles. Once the triangle is solved, its sides also determine its area, perimeter, height, and circle radii.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.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>Right Triangle \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> the default values are Leg a = 3 and Leg b = 4. Find the remaining measurements.<\/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>Result:<\/strong> the sides are 3, 4, and 5 units; the acute angles are approximately 36.8699\u00b0 and 53.1301\u00b0. The area is 6 square units and the perimeter is 12 units.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter two known measurements, including at least one side. The side fields are <strong>Leg a<\/strong>, <strong>Leg b<\/strong>, and <strong>Hypotenuse c<\/strong>. Leg a is opposite Angle \u03b1; Leg b is opposite Angle \u03b2.<\/li>\n<li>For a side-and-angle calculation, enter a side and either <strong>Angle \u03b1<\/strong> or <strong>Angle \u03b2<\/strong> in degrees. Alternatively, pair a side with <strong>Area<\/strong> or <strong>Perimeter<\/strong>. Enter all side lengths in the same unit and area in its corresponding square unit.<\/li>\n<li>Clear the default values in <strong>Leg a<\/strong> and <strong>Leg b<\/strong> if they are not among your known measurements. Leave fields you do not want to use empty.<\/li>\n<li>Read <strong>Solved Triangle<\/strong> for the sides, angles in degrees and radians, area, perimeter, height to hypotenuse, inradius, and circumradius. Check <strong>Measurements used<\/strong> to see which inputs determined the result.<\/li>\n<\/ol>\n<h2>What the solved triangle tells you<\/h2>\n<p>A right triangle has one 90\u00b0 angle. Its two legs meet at that angle, and the hypotenuse is the side opposite it. The acute angles \u03b1 and \u03b2 add to 90\u00b0. Knowing two suitable measurements, at least one of them a side, usually fixes both the triangle\u2019s shape and its size. Two angles alone fix the shape but cannot determine side lengths.<\/p>\n<p>The hypotenuse can be found from two legs using \\(a^2+b^2=c^2\\). If a leg and an acute angle are known, trigonometric ratios relate them to the other sides. For example, \\(\\tan\\alpha=a\/b\\) and \\(\\sin\\alpha=a\/c\\). For a focused calculation using these relationships, see the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/pythagorean-theorem-calculator\/\">Pythagorean Theorem Calculator<\/a> or <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/trigonometry-calculator\/\">Trigonometry Calculator<\/a>.<\/p>\n<p>The area is half the product of the legs because they serve as a perpendicular base and height. The reported <strong>Height to hypotenuse<\/strong> is a different height: it runs from the right-angle vertex to the hypotenuse. The inradius is the radius of a circle touching all three sides; the circumradius is the radius of a circle passing through all three vertices. In a right triangle, the circumradius always equals half the hypotenuse. If you only need area from a different set of triangle measurements, use the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/triangle-area-calculator\/\">Triangle Area Calculator<\/a>.<\/p>\n<h2>Input rules and practical limits<\/h2>\n<p>Enter positive, finite measurements. Each acute angle must be greater than 0\u00b0 and less than 90\u00b0, and the hypotenuse must be longer than either known leg. A side paired with area or perimeter must also describe a possible right triangle; the calculator reports an error when it does not.<\/p>\n<p>The calculator uses only two entered values. It takes the first two available sides in the order Leg a, Leg b, Hypotenuse c. If only one side is entered, it pairs that side with the first available value in this order: Angle \u03b1, Angle \u03b2, Area, Perimeter. Other entries are ignored rather than checked for consistency, so clear unwanted fields and consult <strong>Measurements used<\/strong>.<\/p>\n<p>A hypotenuse paired with an area or perimeter can allow two labelings of the same shape: swapping legs a and b also swaps angles \u03b1 and \u03b2. The result and scaled drawing show the labeling with \\(a\\leq b\\); a note under <strong>Measurements used<\/strong> identifies when the swapped labeling is also possible. The drawing is scaled to show proportions, not to provide a physical measurement at screen size.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solve a right triangle from two known measurements, including at least one side. Enter side lengths, an acute angle, area, or perimeter to find the remaining measurements.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[23],"class_list":["post-67162","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-geometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=67162"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67162\/revisions"}],"predecessor-version":[{"id":67211,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/67162\/revisions\/67211"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=67162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=67162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=67162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}