Measuring mountains
Have you ever wondered how people measure the height of a mountain?
They don’t do it by climbing the mountain and measuring with a ruler
as they go! The height of a mountain is found by measuring angles.
Engineers and surveyors use a theodolite to measure angles and
distances. This surveyor is using a theodolite at a building site.
What you will need
a piece of thick cardboard
a plastic or paper drinking straw
scissors
a small screw
a tape measure, yardstick, or meter stick
thread
transparent tape
Perhaps there are no mountains where you live, but there are certainly
trees, flagpoles, lampposts and other tall things. Would you like to
know how to use angles to find out how tall these things are?
First, you have to make a theodolite (thee [ahd]{.smallcaps} uh lyt),
which is a tool for finding angles. Of course, your homemade theodolite
will be a very simple one. People who actually measure the height of
mountains and the size of large areas of land use a very complicated
theodolite. Such a theodolite has a telescope, and number scales with
which angles and distances can be measured. Even so, your theodolite
will do the same basic job as theirs.
You will find it very easy to make your own theodolite. The things you
will need to make it are listed here. The piece of cardboard should be
fairly thick and at least six inches (15 centimeters) in length and
width.
Cut the cardboard so that you have a square that measures about 6 inches
(15 centimeters) on each side. Then, cut the square in half, slantwise,
from one corner to the other, so that you have two right triangles.
Using some pieces of transparent tape, fasten the straw along the long
edge of one of the triangles.
Cut off a piece of thread about 10 inches (25 centimeters) long. Tie the
screw to one end of the thread.
Using one or two pieces of transparent tape, fasten the other end of the
thread under the top end of the straw, so that the thread hangs straight
down along the edge of the triangle.
To use the theodolite, pick out a tall object such as a tree, or
building, or flagpole. Raise the theodolite to your eye. Hold the
theodolite so that the thread hangs straight down along the edge of the
cardboard triangle. If it hangs away from the triangle, either to the
front or to the side, move the triangle until the thread hangs straight
down the edge of the triangle.
Looking through the straw, and keeping the thread straight, move
backward or forward until you can see the very top of the object you
want to measure.
From where you are, an imaginary line stretches on an angle from your
eye to the top of the object you’re measuring. Another imaginary line,
this one level, goes from your eye to the object.
These imaginary lines form an angle. Your cardboard theodolite has a
fixed angle of 45 degrees because of its shape. This is why you don\’t
have to measure the angle.
All you have to do now is use the tape measure, or measuring stick, to
measure the distance from where you are standing to the bottom of the
object you are looking at. To this distance, you have to add your
height. The total of these two numbers is the height of the object
you’re measuring— whether it’s a tree or a mountain!
If the object you are measuring is 45 feet away, and you are five feet
tall, you know that the object is 50 feet high.
