Return to Mathematics IndexMeasurement of Objects Using Similar Triangles in The Plane

John Gabrielson Chicago H. S. for Agri. Science

3807 W. 111th Street

Chicago IL 60655

(312)535-2500Objectives:

The students in the high school geometry class will apply the use of similar

triangles to a sight tool in order to measure the distance between, or height

of large objects such as buildings or trees.

Materials Needed:

(Dimensions used can be adjusted for own use)

1/2 inch plastic tubing cut into 2' length for sight tube

1" x 2" x 4' wood base and arm

29cm x 33cm cardboard squares

30cm string cord

Washer weight

Bolt with wing nut and locking washer

Copy of centimeter ruler

Long tape measureStrategy:

Construction of this measuring tool involves fastening two 1" x 2" x 4'

boards with bolt wing nut and locking washer placed together approximately one

inch from the end of both boards. This will form the one arm and the base of

the tool.

The 30cm string cord with a washer weight is attached to upper left hand

corner of the 29cm x 33cm card. This card with weighted cord is attached over

the head of the bolt of the measuring tool at the edge of the joined stick. A

sight tube is glued onto the arm above the attached card at the top corner edge

of the joined stick. This forms the top upper corner of the measuring tool.

Leveling the measuring tool will set the position where the weighted cord

crosses the bottom of the card in a position exactly even with the position of

its attachment to the top corner of the card. This will help determine where

the zero position of the copy of the centimeter ruler should be glued.

An angle of elevation will be formed by looking through the sight tube.

The top of an object observed will form the local point. This is point b of the

triangle. A line can be imagined across from the eye of the observer to the

object observed. On this object point c can be named. The eye of the observer

forms point a. A large triangle has been formed by the thought process of

connecting the points from the eye of the observer, to the top of the object

observed, to the eye level on the object, back to the observer.

A second triangle similar to the above triangle will be formed onto the

cardboard card attached to the measuring devise. When the measuring devise is

elevated the cord will move across the centimeter ruler glued at the bottom of

the card. When the cord stops moving, it will provide the measurement of a

side. Label this crossing, point e. Point d can be named at the top of the

where the cord is attached. Point f can be named at the bottom corner of the

card where the card forms a right triangle. Segment df will be the side of the

card and the other side of the small triangle segment ef will be the measurement

along the centimeter ruler.

In order to solve these similar triangles the observers will have to know

either the height of the object to find the distance or the distance to the

object to find the height. One then can set up the equality:

bc_{=}ac.

ef df

Having three knowns, two on the card, and one from the triangle of the object

observed, one can solve the problem.

The teacher will use this tool in a lesson to instruct students about

similar triangles. The students can be taught the concept of similar triangles

using a proportional growth pattern of triangles. This can be followed by

instructional use of the tool. The students are then to be brought outside and

begin the actual computation of similar triangles by using the measuring tool.Performance Assessment:

The students can be evaluated in groups. Collection of group work will reveal

how accurately the measurements were taken. Correct mathematics can also be

checked. The scores given can then be recorded and individuals will be given a

group grade.