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	<title>Ask the GPS Expert &#187; Geocaching</title>
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		<title>Geocaching Puzzle Caches: How to find the Orthocenter of a Triangle</title>
		<link>http://blog.expertgps.com/blog/2009/03/geocaching-puzzle-caches-how-to-find-the-orthocenter-of-a-triangle/</link>
		<comments>http://blog.expertgps.com/blog/2009/03/geocaching-puzzle-caches-how-to-find-the-orthocenter-of-a-triangle/#comments</comments>
		<pubDate>Tue, 24 Mar 2009 17:26:36 +0000</pubDate>
		<dc:creator>Dan Foster</dc:creator>
				<category><![CDATA[Geocaching]]></category>
		<category><![CDATA[area]]></category>
		<category><![CDATA[cache]]></category>
		<category><![CDATA[GeoBuddy]]></category>
		<category><![CDATA[orthocenter]]></category>
		<category><![CDATA[puzzle]]></category>
		<category><![CDATA[triangle]]></category>

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		<description><![CDATA[

Herb asks:
How do I find the orthocenter of the triangle created by three waypoints?



The orthocenter of a triangle is located at the intersection of the three lines.  Each line runs through a vertex and is perpendicular to the opposite side.
Let's solve a geocaching puzzle cache that requires us to find the orthocenter of a [...]]]></description>
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<!--noteaser-->
<p class="question"><b>Herb asks:</b><br />
<img src="http://www.expertgps.com/images/open-quote.png" alt="quote" />How do I find the orthocenter of the triangle created by three waypoints?<img src="http://www.expertgps.com/images/close-quote.png" alt="quote" />
</p>
<br />
<img class="right" src="http://blog.expertgps.com/images/orthocenter-3.png" alt="Finding the orthocenter - geocaching puzzle cache geometry" width="263" height="227" />
<p>The orthocenter of a triangle is located at the intersection of the three lines.  Each line runs through a vertex and is perpendicular to the opposite side.</p>
<p>Let's solve a geocaching puzzle cache that requires us to find the orthocenter of a triangle.  By adding the three waypoints to a closed route in ExpertGPS or GeoBuddy, we can calculate the bearings along each edge of the triangle.  By adding 90 degrees to each bearing, we can determine the direction of a line perpendicular to that edge.  Now we can use the <b>Project Waypoint dialog</b> to project a line from the opposite vertex.</p>
<img src="http://blog.expertgps.com/images/orthocenter-1.png" alt="Solving geocaching puzzles: calculating the orthocenter of a triangle" width="411" height="334" />
<p>In the second screenshot, I'm projecting a line from waypoint 1 at 111.23 degrees (which is 90 degrees more than the bearing of the opposite edge - 21.23 degrees).  Repeat three times, creating a new route between the vertex and the newly-projected waypoint, and you've found the orthocenter.</p>
<img src="http://blog.expertgps.com/images/orthocenter-2.png" alt="Finding orthocenter" width="537" height="532" />
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