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129 lines
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HTML
129 lines
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HTML
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<title>Solving Triangles by Reflection</title>
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<h1 align="center">Solving Triangles by Reflection</h1>
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<table width="95%" align="center">
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<tr><td><img src="images/trig-ladder.gif" alt="ladder against wall" width="224" height="179" /></td>
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<td><p>A 5ft ladder leans against a wall as shown. </p>
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<p>What is the <b>angle</b> between the ladder and the wall? </p></td>
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</tr></table>
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<p>This is surprisingly easy to solve by using <a href="../geometry/reflection.html">Reflection</a>:</p>
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<table width="90%" align="center">
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<tr>
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<td align="right"><p>Here is the triangle with its reflection</p>
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<p>Together they make an <a href="../triangle.html">equilateral triangle</a> (all sides equal).</p></td><td><img src="images/trig-ladder3.gif" width="162" height="162" alt="trig ladder symmetry is equilateral triangle" /> </td>
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<tr>
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<td><img src="../images/triangle-equilateral.gif" width="150" height="106" alt="Equilateral Triangle" /></td>
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<td>The angles in an <br />
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equilateral
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triangle<br />
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are all 60°</td>
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</tr>
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</table>
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<table width="90%" border="0" align="center">
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<tr>
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<td><img src="images/trig-ladder4.gif" width="161" height="150" alt="trig ladder symmetry is equilateral triangle" /></td>
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<td><p> </p>
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<p>So the angle between the ladder and the wall is <b>half of 60°</b> </p>
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<p align="center" class="large">= 30°</p></td>
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</tr>
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</table>
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<h2>Finding Length</h2>
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<p>
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<b>We can use the same idea to find an unknown length.</b></p>
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<p style="float:left; margin: 0 10px 5px 0;"><img src="images/trig-tree.gif" width="256" height="131" alt="trig tree 42m at 30 degrees" /></p>
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<p>Alex has a laser that measures distance. </p>
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<p>By standing some distance from the tree Alex measures <span class="large">42m</span> to the top of the tree at an angle of <span class="large">30°</span>. </p>
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<p>What is the height of the tree?</p>
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<p>Here is the triangle and its reflection:</p>
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<table align="center"><tr><td><img src="images/trig-tree2.gif" alt="trig tree symmetry is equilateral triangle on side" /> </td>
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<td><p>Once again the triangle and its reflection make an equilateral triangle.</p>
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<p>So, we know the height of the tree must be <b>half of 42m</b></p>
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<p align="center" class="large">= 21m</p></td>
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</tr></table>
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<p>These examples show that the same triangle can occur in many different situations!</p>
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<p> </p>
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<script type="text/javascript">getQ(730, 731, 7873, 7874, 7875, 7876, 7877, 7878, 1498, 1499);</script>
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<div class="related">
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<a href="trig-sine-law.html">The Law of Sines</a>
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<a href="trig-cosine-law.html">The Law of Cosines</a>
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<a href="trig-solving-triangles.html">Solving Triangles</a>
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<a href="trigonometry-index.html">Trigonometry Index</a>
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<a href="index.html">Algebra Index</a> </div>
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