# Ptolemy's Ptools

## Triangulating Project:

In this project we will find the distance across a creek (or ?) without going to the other side.

Materials Needed;

 35 cm X 35 cm rigid cardboard (14" X 14") 2 straight sticks (like broom handles) clipboard, paper & pencil

The Plan;

 Prepare Ahead:Choosing a Site: Set the project up in an open, flat area. You will need to set your observation stations up along the side of the area being measured with at least as much distance between stations as the area being measured is wide. Preliminary Preparation: Indoors, make a jumbo protractor on the cardboard by gluing a quadrant copy onto it and extending the 10 degree lines out using the ruler. The larger the better. Make the "0" line (base line) extra dark. Collecting the Data: Locate a stationary object near the adjacent bank for sighting purposes. Push one stick into the ground so that it stands straight up on its own, directly across the creek from the object chosen (This will be station #1) Placing the jumbo protractor flat over this stick (horizontal); form a 90 degree angle with the object on the opposite bank and the other stick, held at least as far away (along the side of the bank) as the creek is wide. Choosing a convenient (whole #) distance between sticks, push the second stick into the ground so that it stands straight on its own (This will be station #2) Sight the object with the jumbo protractor on the second stick to find the degree measure from the base line you made with the two sticks to the object across the creekProcessing the Data: Look up the Tangent Ratio for the angle measured and MULTIPLY this by the distance between stations. The result will be the distance across the creek (in whatever units you used to measure the distance between stations).

An EXAMPLE:

to Tangent Tables

How it works; Using the Properties of Triangles

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