Skip to content

HTTPS clone URL

Subversion checkout URL

You can clone with HTTPS or Subversion.

Download ZIP
Fetching contributors…

Cannot retrieve contributors at this time

99 lines (82 sloc) 4.04 kb
<!DOCTYPE html>
<html data-require="math graphie math-format">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Pythagorean theorem 1</title>
<script src="../khan-exercise.js"></script>
<script>
function betterTriangle(width, height, A, B, C, a, b, c) {
var scale = 5 / Math.sqrt(width * width + height * height);
width *= scale;
height *= scale;
with ( KhanUtil.currentGraph ) {
// Leave some space for the labels
init({ range: [[-1.5, width + 1], [-1, height + 1]] });
path([ [0, 0], [width, 0], [0, height], true ]);
label( [0, height], A, "above left" );
label( [0, 0], C, "below left" );
label( [width, 0], B, "below right" );
label( [0, height/2], b, "left" );
label( [width/2, 0], a, "below" );
label( [width/2, height/2], c, "above right", {
labelDistance: 3
} );
}
}
</script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="find-hypotenuse">
<div class="vars">
<var id="AC">randRange(3, 8)</var>
<var id="BC">randRange(3, 8)</var>
<var id="AB2">AC * AC + BC * BC</var>
</div>
<div class="question">
<p>In the right triangle shown, <code>AC = <var>AC</var></code> and
<code>BC = <var>BC</var></code>. What is <code>AB</code>?</p>
<div class="graphie">
betterTriangle( BC, AC, "A", "B", "C", BC, AC, "?" );
</div>
</div>
<div class="solution" data-type="radical"><var>AB2</var></div>
<div class="hints" data-apply="appendContents">
<p>We want to find <code>c</code>; let <code>a = <var>BC</var></code> and <code>b = <var>AC</var></code>.</p>
<p>So <code>c^2 = <var>BC</var>^2 + <var>AC</var>^2 = <var>AB2</var></code>.</p>
<p>Then, <code>c = \sqrt{<var>AB2</var>}</code>.</p>
<p data-if="squareRootCanSimplify(AB2)">Simplifying the radical gives <code>c = <var>formattedSquareRootOf(AB2)</var>.</code></p>
</div>
</div>
<div id="find-a-leg">
<div class="vars">
<var id="AC">randRange(3, 5)</var>
<var id="AB">randRange(6, 10)</var>
<var id="BC2">AB * AB - AC * AC</var>
<var id="legs">shuffle([["a", "?", "BC", sqrt(BC2)], ["b", AC, "AC", AC]])</var>
<var id="a, alabel, aside, alen">legs[0]</var>
<var id="b, blabel, bside, blen">legs[1]</var>
</div>
<div class="question">
<p>In the right triangle shown, <code><var>bside</var> = <var>AC</var></code> and
<code>AB = <var>AB</var></code>. What is <code><var>aside</var></code>?</p>
<div class="graphie">
betterTriangle( alen, blen, "A", "B", "C", alabel, blabel, AB );
</div>
</div>
<div class="solution" data-type="radical"><var>BC2</var></div>
<div class="hints" data-apply="appendContents">
<p>We want to find <code><var>a</var></code>; let <code><var>b</var> = <var>AC</var></code> and <code>c = <var>AB</var></code>.</p>
<p>So <code><var>a</var>^2 = c^2 - <var>b</var>^2 = <var>AB</var>^2 - <var>AC</var>^2 = <var>BC2</var></code>.</p>
<p>Then, <code><var>a</var> = \sqrt{<var>BC2</var>}</code>.</p>
<p data-if="squareRootCanSimplify(BC2)">Simplifying the radical gives <code><var>a</var> = <var>formattedSquareRootOf(BC2)</var>.</code></p>
</div>
</div>
</div>
<div class="hints">
<p>We know <code>a^2 + b^2 = c^2</code>.</p>
</div>
</div>
</body>
</html>
Jump to Line
Something went wrong with that request. Please try again.