A sextant is an instrument used to indirectly measure distances. A measuring tape or meter stick is incapable of measuring the distance to a star. Sextants have been used for centuries to make this sort of indirect measurement. In this activity sextants will be made and used to measure the height of a very tall object, such as a flagpole or a building.

Materials

Protractor

Straight plastic drinking straw

Tape

String

Metal washer

Metal stick or tape measure

Graph paper

What To Do

Tie a piece of string around the washer and tie the other end of the string through the hole in the flat side of the protractor so that the washer hangs from the protractor. The string should be long enough so that when the protractor is held upside down the washer hangs below the curved edge of the protractor by at least an inch. Tape the straw across the middle of the protractor. One end of the straw should cross the hole where the string is tied, and the other end of the straw should cross the curved side at the ninety-degree mark. Equal lengths of the straw should extend past the protractor on both sides. The sextant is ready for use.

Decide what object you would like to use for the height measurement. Mark a spot on the ground that is 10 meters away from the object. Ask one student to hold a meter stick upright at the spot 10 meters from the object. At the marked spot hold the sextant just above the meter at a height one meter above the ground, squat down to look through the straw on the curved side of the protractor to sight the top of the object being measured. While looking at the top of the tall object through the straw on the sextant, have a partner record the number on the protractor across which the string hangs. The height of the tall object is determined by making a scale drawing on graph paper. Draw a horizontal line ten squares long across the center of the paper. This represents the ten-meter distance between the object and the location at which the measurement was made. Draw a long vertical line at the left end of the horizontal line to represent the tall object. It should look like a large L. At the right end of the horizontal line draw a line at the same angle that was recorded when the tall object was measured. Use the protractor to measure the angle and draw the line long enough so that it crosses the vertical line on the left. Count the number of squares between the intersections of the horizontal and angled lines. This represents the height of the measured object. Add one more square to your final count of squares along the vertical. Remember the measurement was taken from one meter above the ground.

Questions

1. Why are sextants used to measure the heights of very tall objects? Would any other method be easier? Would it be as safe?

2. Why did the measurement with the sextant have to be made a certain distance from the base of the object being measured? Must that distance be exactly 10 meters, or could it be a longer or shorter distance instead?

3. If the same object was sighted twice, once from five meters and once from ten meters, would the measured angles be equal? If not, how would they differ?

4. If the same object was sighted twice, once from five meters and once from ten meters, would the values obtained for the height of the object be the same?

Summary

Sextants are simple, useful measuring instruments. The height of a very tall object, such as a building, can be determined by making three easy measurements. First, a distance measurement must be made to mark a spot a certain distance from the object being measured (which in this case is ten meters, but could be any distance). The second necessary measurement is a height. The height at which the sextant is held above the ground while the measurement is being made is important because it will be added into the height determined by the graph. Third, an angle must be measured. When the sextant is tilted to see the top of the object through the straw the string, weighted by the washer, still hangs straight down. The number across which the string hangs indicates the angle at which the sextant is tilted. The angle is the angle of elevation that is used in the scale drawing. Once the three measurements have been made, they can be used to determine the height of the object in question. Using the graph paper helps with the scale. In the procedure above, the ten-meter distance away from the object was drawn as a ten-square line. This means that every square on the graph paper stands for one meter in each direction. By drawing the angled line to intersect with the vertical line, the top of the object can be represented by the intersection of the two lines. To draw the angled line, center the straight side of the protractor on the right end of the line. On the curved edge of the protractor, find the number that represents the measured angle, and make a mark. Then use a ruler to draw a line connecting the right end of the horizontal line and the mark made for the angle. Extend this line until it intersects the vertical line on the left. Count the number of squares between the intersections and add the height above the ground at which the measurement was made, and that is the height of the object.

Sources

"Best of Wonder Science." Delmar Publishers, Albany, 1997. ISBN 0-8273-8094-1

"Science for Children: A Book for Teachers." Willard J. Jacobson and Abbey Barry Bergman, Prentice Hall: Englewood Cliffs.

© S. Olesik, WOW Project, Ohio State University, 1999.