{"id":156006,"date":"2022-03-26T01:16:36","date_gmt":"2022-03-25T19:46:36","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/arc\/"},"modified":"2024-08-29T16:20:11","modified_gmt":"2024-08-29T10:50:11","slug":"arc","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/arc\/","title":{"rendered":"What is Arc? (Arc Length, Arc Angle, Arc of Circle, Examples)"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#What_is_Arc\" title=\"What is Arc ?\">What is Arc ?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#What_is_Arc_Length\" title=\"What is Arc Length?\">What is Arc Length?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#Arc_Length_Formula\" title=\"Arc Length Formula\">Arc Length Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#Types_of_Arcs\" title=\"Types of Arcs\">Types of Arcs<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#Applications_of_Arcs\" title=\"Applications of Arcs\">Applications of Arcs<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#Arc_Solved_Examples\" title=\"Arc Solved Examples\">Arc Solved Examples<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#Arc_Practice_Question\" title=\"Arc Practice Question\">Arc Practice Question<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#Arc_FAQs\" title=\"Arc FAQs\">Arc FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#What_is_the_formula_to_calculate_arc_length_in_radians\" title=\"What is the formula to calculate arc length in radians?\">What is the formula to calculate arc length in radians?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#How_do_you_find_the_arc_length_if_the_central_angle_is_given_in_degrees\" title=\"How do you find the arc length if the central angle is given in degrees?\">How do you find the arc length if the central angle is given in degrees?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#What_is_the_difference_between_a_Major_Arc_and_a_Minor_Arc\" title=\"What is the difference between a Major Arc and a Minor Arc?\">What is the difference between a Major Arc and a Minor Arc?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/arc\/#What_is_the_inscribed_angle\" title=\"What is the inscribed angle?\">What is the inscribed angle?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Arc\"><\/span>What is Arc ?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Arc length refers to the distance measured along a curved path or the circumference of a circle. It\u2019s the length of the curved segment, known as the arc. This distance will always be longer than the straight line connecting the two endpoints of the arc, called the chord.<\/p>\n<p>To calculate the length of an arc in a circle with radius r, you use different formulas depending on whether the angle is given in degrees or radians.<\/p>\n<ul>\n<li><strong>When the angle is in degrees:<\/strong><br \/>\nThe formula for arc length is: Arc Length = \ud835\udc5f \u00d7 \ud835\udf03 \u00d7 (\ud835\udf0b180)<br \/>\nHere, \u03b8 is the angle in degrees. The term \ud835\udf0b180 converts degrees to radians, which is necessary for the calculation.<\/li>\n<li><strong>When the angle is in radians:<\/strong><br \/>\nThe formula simplifies to: Arc Length = \ud835\udc5f \u00d7 \ud835\udf03<br \/>\nIn this case, \u03b8 is already in radians, so no conversion is needed.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Arc_Length\"><\/span>What is Arc Length?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-731178\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/What-is-Arc-Length.png\" alt=\"What is Arc Length\" width=\"216\" height=\"205\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/What-is-Arc-Length.png 216w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/What-is-Arc-Length-150x142.png 150w\" sizes=\"(max-width: 216px) 100vw, 216px\" \/><\/p>\n<p>Arc length is the measure of the distance along a curved section of a circle or any curve. It represents the space between two points along this curved path. For a circle, the arc is simply a segment of its circumference.<\/p>\n<p>When discussing arc length, the angle subtended by the arc at the centre of the circle plays an important role. This angle is formed by the two line segments that extend from the circle&#8217;s centre to the endpoints of the arc.<\/p>\n<p>For instance, consider a circle where OP is an arc with the centre Q. The length of the arc OP, denoted as L, is the distance you would measure along the curve between the two endpoints of OP.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Arc_Length_Formula\"><\/span>Arc Length Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To derive the formula for arc length, we start by recalling the formula for the circumference of a full circle, which is 2\u03c0r, where r is the radius of the circle. The arc is simply a portion of this circumference.<\/p>\n<p><strong>Arc Length in Degrees:<\/strong><br \/>\nA full circle subtends an angle of 360\u00b0. If the angle subtended by the arc is \u03b8, then the arc represents a fraction \u03b8360 of the total circumference.<\/p>\n<p>Therefore, the formula for the arc length L when \u03b8 is in degrees is:<br \/>\nArc Length = \u03b8\/360 \u00d7 2\u03c0r = r\u03b8\u03c0180\u200b<\/p>\n<p><strong>Arc Length in Radians:<\/strong><br \/>\nIf the angle is given in radians, the calculation becomes simpler. In radians, the angle subtended by the arc is already in the appropriate unit for the formula.<br \/>\nFor an angle \u03b8 in radians, the formula for arc length L is:<br \/>\n<strong>Arc Length=r\u03b8<\/strong><br \/>\nThis is derived from the fact that 1 radian subtends an arc length equal to the radius of the circle.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Arcs\"><\/span>Types of Arcs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Arcs are segments of a circle\u2019s circumference and can be categorised into different types based on their length and angle. These types are described as follows.<\/p>\n<ul>\n<li><strong>Minor Arc<\/strong><br \/>\nA Minor Arc is an arc that measures less than half of the circle\u2019s circumference. The central angle of a Minor Arc is less than 180\u00b0. For example, in a given circle, if an arc is subtended by an angle less than 180\u00b0, it is considered a Minor Arc. The length of a Minor Arc is calculated using the central angle of the arc which is less than 180\u00b0.<\/li>\n<li><strong>Major Arc<\/strong><br \/>\nA Major Arc spans more than half of the circle\u2019s circumference. The central angle of a Major Arc is more than 180\u00b0. In a given circle, if an arc subtends an angle greater than 180\u00b0, it is a Major Arc. The measure of a Major Arc can be determined by subtracting the measure of the Minor Arc from 360\u00b0. For example, if the Minor Arc is 120\u00b0, the Major Arc would be 360\u00b0 &#8211; 120\u00b0 = 240\u00b0.<\/li>\n<li><strong>Semicircle<\/strong><br \/>\nA Semicircle is an arc that measures exactly 180\u00b0. A Semicircle represents exactly half of a circle when it is divided along its diameter. This means it covers the entire half of the circle\u2019s circumference. The length of a Semicircle is half of the circle\u2019s total circumference.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Applications_of_Arcs\"><\/span>Applications of Arcs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Arcs play a significant role in various fields due to their structural properties.<\/p>\n<ol>\n<li>Arcs are commonly used in the design of bridges, allowing them to span streams, rivers, and other gaps efficiently.<\/li>\n<li>Arcs are integral to creating arches over doorways, and windows, and forming domes in buildings, enhancing both functionality and visual appeal.<\/li>\n<li>Design and Communication.<\/li>\n<li>Arcs contribute to the aesthetic elements of buildings and structures, improving their visual harmony.<\/li>\n<li>The design of arcs aids in the efficient transmission of TV and radio signals through high-speed cables.<\/li>\n<li>The traditional bow used by archers features a prominent arc, which is crucial for its design and performance.<\/li>\n<li>When an object such as a coin or stone is tossed into the air, it follows a curved arc due to the force of gravity.<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"Arc_Solved_Examples\"><\/span>Arc Solved Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Example: A circle with a radius of 5 units and a central angle of 60\u00b0 is given. Find the length of the Minor Arc.<\/strong><\/p>\n<p>Solution:  Angle in Radians = pi\/3<\/p>\n<p>Use the Arc Length Formula: Arc Length=r\u03b8<br \/>\nwhere \u03b8 is in radians.<br \/>\nNow, Substitute the Values:<br \/>\nArc Length=r\u03b8 = 5 * pi\/3 = 5.24<br \/>\nThus, the length of the Minor Arc is approximately 5.24 units.<\/p>\n<p><strong>Example: A circle with a radius of 8 units and a central angle of 120\u00b0. Find the length of the Major Arc.<\/strong><\/p>\n<p>Solution: Arc Length = \u03b8\/360 \u00d7 2\u03c0r = r\u03b8\u03c0\/180\u200b<br \/>\nwhere \u03b8=120<br \/>\nArc Length = \u03b8\/360 \u00d7 2\u03c0r = r\u03b8\u03c0\/180 = 8 (120) \u03c0\/180 = 8.38 units\u200b<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Arc_Practice_Question\"><\/span>Arc Practice Question<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Q. 1. A circle with a radius of 10 units and a central angle of 3 radians. Find the length of the arc.<br \/>\nQ. 2. A circle with a radius of 6 units and an arc length of 15 units. Find the central angle (in radians) subtended by the arc.<br \/>\nQ. 3. A circle with a radius of 4 units and a central angle of 150\u00b0. Find the length of the Major Arc.<br \/>\nQ. 4. A circle with a radius of 5 units and a chord length of 6 units. Find the central angle (in radians) subtended by the chord.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Arc_FAQs\"><\/span>Arc FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_formula_to_calculate_arc_length_in_radians\"><\/span>What is the formula to calculate arc length in radians?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo calculate the arc length when the central angle is in radians, use the formula: Arc Length=\u03b8\u00d7r where \u03b8 is the central angle in radians and r is the radius of the circle.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_find_the_arc_length_if_the_central_angle_is_given_in_degrees\"><\/span>How do you find the arc length if the central angle is given in degrees?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tWhen the central angle is in degrees, use the formula: Arc Length = \ud835\udc5f \u00d7 \ud835\udf03 \u00d7 (\ud835\udf0b180) where \u03b8 is the central angle in degrees and r is the radius of the circle.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_difference_between_a_Major_Arc_and_a_Minor_Arc\"><\/span>What is the difference between a Major Arc and a Minor Arc?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\t Minor Arc: An arc that measures less than 180\u00b0 of the circle\u2019s circumference. It is the shorter of the two arcs connecting the same endpoints. Major Arc: An arc that measures more than 180\u00b0 of the circle\u2019s circumference. It is the longer arc connecting the same endpoints.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_inscribed_angle\"><\/span>What is the inscribed angle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe angle subtended by the arc at any point on the circumference of the circle is called an inscribed angle. Find the arc length of a circle that subtends an angle of 120\u00b0 to the center of a circle whose radius is 24 cm. The length of an arc = 2\u03c0r(\u03b8\/360) = 2 x 3.14 x 24 x 120\/360 = 50.24 cm\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the formula to calculate arc length in radians?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To calculate the arc length when the central angle is in radians, use the formula: Arc Length=\u03b8\u00d7r where \u03b8 is the central angle in radians and r is the radius of the circle.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you find the arc length if the central angle is given in degrees?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"When the central angle is in degrees, use the formula: Arc Length = \ud835\udc5f \u00d7 \ud835\udf03 \u00d7 (\ud835\udf0b180) where \u03b8 is the central angle in degrees and r is the radius of the circle.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the difference between a Major Arc and a Minor Arc?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Minor Arc: An arc that measures less than 180\u00b0 of the circle\u2019s circumference. It is the shorter of the two arcs connecting the same endpoints. Major Arc: An arc that measures more than 180\u00b0 of the circle\u2019s circumference. It is the longer arc connecting the same endpoints.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the inscribed angle?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The angle subtended by the arc at any point on the circumference of the circle is called an inscribed angle. Find the arc length of a circle that subtends an angle of 120\u00b0 to the center of a circle whose radius is 24 cm. The length of an arc = 2\u03c0r(\u03b8\/360) = 2 x 3.14 x 24 x 120\/360 = 50.24 cm\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>What is Arc ? Arc length refers to the distance measured along a curved path or the circumference of a [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Arc Introduction","_yoast_wpseo_title":"Arc, Arc Length, Arc Angle, Arc of Circle, Examples | Infinity Learn","_yoast_wpseo_metadesc":"The arc of a circle is the portion of the circle between two points on the circle, the endpoints of the arc at Infinitylearn.com.","custom_permalink":"maths\/arc\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Arc, Arc Length, Arc Angle, Arc of Circle, Examples | Infinity Learn<\/title>\n<meta name=\"description\" content=\"The arc of a circle is the portion of the circle between two points on the circle, the endpoints of the arc at 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