Triangulation

Brandon, Ann M.W.                   Oak Forest High School
                                    687-0500
                           

Objectives:  
The student will learn the basics of how to perform and calculate 
triangulation 

Materials:  
1 small pizza box; 1 soda straw; 1 paper protractor; 1 straight pin, 
large head; some centimeter tape; some string; a stapler or masking 
tape; some super glue ("Krazy"); and 1 washer. 

Strategy:
MAKE THE BOX:  1) Put box together as manufacturer intended.  2) Bend 
top backwards, at top crease.  Staple under box, forming open end.  3) 
Fold side flaps up and staple near back (closed) end.  4) Punch hole in 
center of back (closed end), near bottom.  5) Glue protractor on inside 
bottom -- center protractor on eye hole.  6) Tie string to pin and eye 
hole.  Length of string should be longer than half the length of the 
box.  7) Glue string to pin.  8) Stretch string and pin to sides of 
box, and mark on each side. 
        |                  |
        |                  |
      A |                  | B
        |\                /|
        | \              / |
        |  \            /  |
        |   \          /   |
        |    \        /    |
        |     \      /     |
        |      \    /      |
        |       \  /       |
        |        \/        |
        --------------------
                 E

9) Place centimeter tape from mark to mark.  10) Cut out side flaps 
back to centimeter tape, fold the remaining inside flaps around and 
tuck into back.  11) Measure the perpendicular distance from eye hole 
to tape and record this on the box.  12)  Tape (glue) straw along back 
edge of box. 

You need a baseline laid out in meters (or feet, or any unit -- even 
sidewalk squares).  "Permanent" Magic Marker used on the sidewalk will 
disappear in less than 1 month. 

Stand at some location on the baseline.  (Record this location number.)  
Hold box level with hole in front of your eye, and edge parallel to 
baseline.  Look toward object and place the pin in your line of sight.  
(You see pin and object in line with each other.)  Record the number 
(on the cm tape) which is under the string.  (Scale number 1.)  Move a 
good distance along the baseline and repeat the sighting.  (Location 2, 
scale 2). 


Subtract the locations (=D Baseline) and the scales (=D Scale).  The 
distance to the object = 

        D Baseline
       ------------  X Length to tape
         D Scale

Why does this work?  We are making use of two "facts":  1) light goes 
in straight lines; and 2) similar triangles have proportional 
dimensions.  So:

     D Scale                D Baseline
    --------      =       -------------
    Len to tape           Distance to object

The first triangle (the small one on the box) has a base along the tape 
(= D Scale) and an altitude (length to tape).  The second triangle has 
a base along the baseline (= D Baseline) and an altitude (= distance to 
object sighted). 

NOTE:  It is not necessary that these be acute triangles.  Obtuse 
triangles work just as well.  You will be finding the distance, D, 
perpendicular to the baseline. 

You will need a table of tangents.  You may call for such a table or 
make one for yourself.