Measuring the Height of Trees and Buildings

When I was teaching junior high and high school classes I would look for lessons that would allow me and the students to get out of the classroom, but still keep them interested. One example was to have students calculate the heights of trees and other tall things like the flagpole, buildings etc. The basic device to do this is called a "hypsometer". A yardstick or meter stick will work and you simply use a process of triangulation.

Yardstick
If you stand exactly 25 feet from a tree to be measured and hold the yardstick with the zero end down toward the ground and hold the yardstick at arm length from you (which should be 25 inches) and line up the bottom view of the yardstick with the base of the tree and then without moving look toward the top of the tree. The point where your upward view crosses the yardstick would then be a measurement in inches. Each inch will be equal to one foot in height for the tree.

If the tree is taller than you can measure begin 25 feet from the tree then move 50 feet away from the tree and now you measure the same way you did before but now multiply the result by 2. If the object is still taller than you can measure you move 75 feet from the object and then multiply your result by 3 etc.

Meter Stick
If you are using a meter stick the procedure is the same but now start by standing 5 meters from the tree with the meter stick 50 centimeters from you (about arm length), line the bottom 0 point with the base of the tree and then sight through to the top of the tree. Each 10 centimeters will equal one meter in the height of the tree. If you are at 10 meters you would double the result; if at 15 meters triple the result; if at 20 meters multiply the result by 4; etc.

These calculations could very easily be put into a spreadsheet and even all the conversions could be done at the same time. You could have students try the meter stick and the yardstick on the same tree. What I did was to go around the area of the school that I wanted to use first and took digital pictures of the trees and buildings I wanted the students to measure. I then made poster signs for each location that indicated "Tree 1"; "Tree 2" etc. I also made a map of the area and indicated the location on the map where each tree (and building) was located that was to be measured. I produced a worksheet with the instructions and a data collection worksheet with the digital pictures of each thing to be measured. I had the students work in groups of three or four and assigned them to a particular starting tree and explained how they would rotate through from location to location. With overhead transparencies they were able to see how the whole process would work. You need to have at least one 50 to 100 foot tape measure for each group. Sometimes these are available in local thrift stores. You can use a 100 foot clothesline that you mark off in 25 foot sections etc. Students were not allowed to go outside the map area and were given a time limit at each station. There were more stations than student groups to allow student movement even should one group finish faster than another group and they all had to complete at least 6 tree measurements. With a class of 30 students then I had at least 10 groups, but had 15-20 stations. Students could move to any station that was not being measured when completing a particular station. They of course were not allowed to copy anything from other groups. They also had to rotate in their group so that each member of the group got a chance to do the sighting and measuring.

Naturally this kind of activity could be done as part of a math or science class, but you may be able to incorporate it into several different subject areas with a bit of creativity. It is fairly easy to check some of these measurements in other ways. For example: If you run one end of a rope up the flagpole you then can measure the rope length that was used and get a pretty good estimate of the height of the flagpole. You can sometimes drop a length of rope from the roof to the ground and get a direct measure of the building height. (We had a custodian drop a length of rope for us.) We did not want students falling from the roof of the school and the custodian was going up there anyway to check for possible leaks.