```TriangulationBrandon, 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,
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.
```