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139 lines
5.3 KiB
HTML
139 lines
5.3 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/geometry/arc.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:34 GMT -->
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<head>
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Arc</title>
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<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, videos and worksheets. For K-12 kids, teachers and parents.">
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<!-- #EndEditable -->
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
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<meta name="HandheldFriendly" content="true">
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<meta name="referrer" content="always">
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<link rel="preload" href="../images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin="">
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<link rel="preload" href="../style4.css" as="style">
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<link rel="preload" href="../main4.js" as="script">
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<link rel="stylesheet" href="../style4.css">
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gtag('js', new Date());
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gtag('config', 'UA-29771508-1');
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</script>
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</head>
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<body id="bodybg">
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<div id="stt"></div>
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<div id="adTop"></div>
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<header>
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<div id="hdr"></div>
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<div id="tran"></div>
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<div id="adHide"></div>
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<div id="cookOK"></div>
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</header>
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<div class="mid">
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
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<div id="search" role="search"></div>
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<div id="linkto"></div>
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<div id="menuSlim" class="menu"></div>
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<div id="menuTiny" class="menu"></div>
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</nav>
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<div id="extra"></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Arc</h1>
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<p class="center larger">Part of the circumference of a <a href="circle.html">circle</a>.<br>
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Or part of any curve.</p>
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<p>See an arc in action (drag the points):</p>
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<div class="script" style="height: 260px;">
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images/circle-prop.js?mode=arc
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</div>
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<h2>Arc Length</h2>
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<p style="float:right; margin: 0 0 5px 10px;"><img src="images/circle-arc-length.svg" alt="circular sector arc length" height="222" width="200"></p>
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<p>The arc length is:</p>
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<p class="center large">L = θ × r <i>(when θ is in radians)</i></p>
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<p class="center large">L = θ × <span class="intbl"><em><span class="times">π</span></em><strong>180</strong></span> × r <i>(when θ is in degrees)</i></p>
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<div style="clear:both">
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</div>
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<div class="script" style="height: 260px;">
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images/circle-prop.js?mode=arclen
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</div>
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<h2>Finding the Radius from Width and Height</h2>
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<p>Say you know the width and height of an arc (maybe it is on the top of a door) and you want to make that arc using some string and a pencil ... what radius do you use?</p>
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<p> </p>
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<p class="center"><img src="images/arc-w-h.svg" alt="arc width and height" height="124" width="214"></p>
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<p class="center larger">radius = <span class="intbl"><em><sup> </sup>height<sup> </sup></em><strong>2</strong></span> + <span class="intbl"><em>width<sup>2</sup></em><strong>8 × height</strong></span></p>
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<p> </p>
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<div class="example">
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<h3>Example: Sam loves this double door, and wants to make one just like it.</h3>
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<p class="center"><img src="images/door-arch.jpg" alt="door arch" height="224" width="240"></p>
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<p>The door width is 1500mm, the side height is 1950mm and total height at center is 2200mm, so:</p>
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<ul>
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<li>The arc width is 1500mm</li>
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<li>The arc height is 2200 − 1950 = 250mm</li>
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</ul>
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<p>Sam calculates the arc radius</p>
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<p class="center larger">radius = <span class="intbl"><em><sup> </sup>250<sup> </sup></em><strong>2</strong></span> + <span class="intbl"><em>1500<sup>2</sup></em><strong>8 × 250</strong></span></p>
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<p class="center larger">radius = 125 + 1125 = 1250</p>
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<p>And it looks like this:</p>
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<p class="center"><img src="images/arc-w-h-example.svg" alt="arc width and height result" height="250" width="250"></p>
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<p>Now Sam can mark out and cut the wood.</p>
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</div>
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<div class="fun">
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<p style="float:right; margin: 10px 0 5px 10px;"><img src="images/circle-intersect-chords-arc.svg" alt="Intersecting chords arc height length radius" height="201" width="201"></p>
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<p>Note: the formula comes from the <a href="circle-intersect-chords.html">Intersecting Chords Theorem</a>, so <b>h(2r-h) = (w/2)(w/2)</b>, can you work out the rest?</p>
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<div style="clear:both"></div>
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</div>
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<p> </p>
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<p> </p>
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<div class="related">
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<a href="circle.html">Circle</a>
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<a href="index.html">Geometry Index</a>
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</div>
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<!-- #EndEditable -->
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</article>
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<div id="adend" class="centerfull noprint"></div>
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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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</div>
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</body><!-- #EndTemplate -->
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<!-- Mirrored from www.mathsisfun.com/geometry/arc.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:37:35 GMT -->
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