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<blockquote data-quote="Jack Simth" data-source="post: 2303053" data-attributes="member: 29252">Ah, but we aren't talking about a set triangle where the question is along the lines of &quot;You can measure this side, estimate these two angles, and need to come up with the exact position of the third point&quot;No, what we have, is something more along the lines of &quot;You can move along this line, and at any point on this line you can approximate the angle to an unknown destination point. Where is the exact position of the destination point?&quot;Here:*: Destination Point________________ tunnel lineA, B, C, D - named points along Tunnel LineNote that this picture is sideways[code]*A___B____C____D____[/code]Okay - so you are moving down the shaft; at point D, you take a reading, and find that you don't have a 30, 45, 60, or 90 degree angle.&nbsp; Oh well, you continue along.&nbsp; A little before C, you have an angle less than 45 degrees.&nbsp; A little beyond, you have more than 45 degrees.&nbsp; 45 degrees is a useful angle, so you go back and forth, and keep checking until you find a C where you have a 45 degree angle.&nbsp; You mark the spot.&nbsp; You continue along, and at B you find you don't have a 30, 45, 60, or 90 degree angle.&nbsp; Oh well, you continue along.&nbsp; When you reach A (in the same way you found C) you capture a 90 degree angle, and mark the spot.&nbsp; Guess what?&nbsp; The distance from A to C is the same as the distance from A to *, and you know the direction from A to *.&nbsp; Congrats, you've found him.How do you measure the angles accurately?&nbsp; Well, it's simple: Standard triangles.&nbsp; You can construct a right triangle by measuring out the sides as length 3, 4, and 5.&nbsp; The specific unit used is completely immaterial - got a dagger?&nbsp; It's length can be your unit.&nbsp; It's fairly simple to come up with a 90 degree angle this way.&nbsp; Once you have a 90 degree angle, you can make a 45 degree angle by measuring out an equal distance along the two edges from the 90 degree angle and connecting them - either corner angle will be 45 degrees.&nbsp; As you are in a shaft that is defined as perfectly vertical, you can use a plumb (a simple weighted cord) to get the reference down, and can thus measure each angle on the same line.</blockquote>

[QUOTE="Jack Simth, post: 2303053, member: 29252"] Ah, but we aren't talking about a set triangle where the question is along the lines of "You can measure this side, estimate these two angles, and need to come up with the exact position of the third point" No, what we have, is something more along the lines of "You can move along this line, and at any point on this line you can approximate the angle to an unknown destination point. Where is the exact position of the destination point?" Here: *: Destination Point ________________ tunnel line A, B, C, D - named points along Tunnel Line Note that this picture is sideways [code] * A___B____C____D____ [/code] Okay - so you are moving down the shaft; at point D, you take a reading, and find that you don't have a 30, 45, 60, or 90 degree angle. Oh well, you continue along. A little before C, you have an angle less than 45 degrees. A little beyond, you have more than 45 degrees. 45 degrees is a useful angle, so you go back and forth, and keep checking until you find a C where you have a 45 degree angle. You mark the spot. You continue along, and at B you find you don't have a 30, 45, 60, or 90 degree angle. Oh well, you continue along. When you reach A (in the same way you found C) you capture a 90 degree angle, and mark the spot. Guess what? The distance from A to C is the same as the distance from A to *, and you know the direction from A to *. Congrats, you've found him. How do you measure the angles accurately? Well, it's simple: Standard triangles. You can construct a right triangle by measuring out the sides as length 3, 4, and 5. The specific unit used is completely immaterial - got a dagger? It's length can be your unit. It's fairly simple to come up with a 90 degree angle this way. Once you have a 90 degree angle, you can make a 45 degree angle by measuring out an equal distance along the two edges from the 90 degree angle and connecting them - either corner angle will be 45 degrees. As you are in a shaft that is defined as perfectly vertical, you can use a plumb (a simple weighted cord) to get the reference down, and can thus measure each angle on the same line. [/QUOTE]

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