Brandon, Ann M.W. Oak Forest High School

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.
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