- To build a theodolite, you will need a protractor, a push pin, string, a weight and a piece of cardboard or wood that is larger than the protractor and cut into the shape of a rectangle. A fishing weight can be used for the weight or you can use another small household object. To use the theodolite, you will need a tangent table, which can be found in trigonometry textbooks or online (see References).
You'll also need a way to measure your distance away from the object whose height you are trying to determine. - Align the straight edge of the protractor along one of the long edges of the cardboard or wooden rectangle, and use the push pin to fasten it into place. The center of the protractor should be at the center of the long side of the rectangle. If you're having trouble inserting the push pin, use a hammer or substitute a small nail in place of the push pin. Tie the weight to one end of the string and tie the other end of the string to the push pin. As you sight along the long edge of the rectangle, the string will hang straight down, helping you find the angle on the protractor.
- To use your theodolite, stand some distance away from the object whose height you are measuring. You'll need to know this distance, or a close approximation, for your later calculations. That figure will be your baseline number. Generally, being farther away is better than being closer as long as you can clearly see the object being measured. Sight along the long edge of the cardboard or wood, aligning it with the top of the object you're measuring. Note the angle as indicated by the string. Look up the angle measurement on the tangent table. Multiply that number by your baseline number, and you will have the height of the object. If the object you are measuring is not stationary, like a rocket for example, you will get more accurate results if several people take measurements from different positions at the same time.