Geometry Distance of Triangles using a Protractor

Eileen Lally                   A. Philip Randolph Magnet School
13801 Kit Lane                 7316 South Hoyne Avenue
Lemont IL 60439                Chicago IL 60636
(630) 257-9389                 (773) 535-9015

Objectives:

Students in the 7th grade are to learn how to use the protractor to measure 
angles, and use this ability to solve a problem involving distance.

Materials Needed:

Protractors for each student
Rulers and meter sticks
Straws and clay

Strategy:

   PART ONE
1. Identify the vocabulary: ray, angle, vertex, unit of measure,  
   protractor
2. Demonstrate or review how to use the protractor.
3. Draw a 60cm line labeled AB on the board.  Instruct students to draw a 6cm 
   line labeled ab on paper.
4. At point A/a make a 35o and at point B/b make a 60o.  Make sure that the rays 
   are extended until they cross.  Label that point C.
5. Compare the triangles (the one on the board and the one on paper).  
   These triangles are similar.
6. Present the question:  What is the distance of the line segment AC without 
   leaving your desk?
7. Set up the ratio:  line AB over line ab = X (AC) over line ac.
8. Now measure the line AC and compare the result with the calculated answer.
   Use the formula: Actual measurement minus Calculated measurement 
   divided by Actual to obtain the margin of error.
   
   PART TWO 
1. Upon a large table, mark two points A and B and determine the distance 
   (AB) between them.

2. Use the protractor to determine the measure of angle BAC.  Likewise, 
   determine the measure of angle ABC. 

3. We now attempt to determine X, the distance (AC) from the point A to the 
   Point C.  Make a model (as described in Part 1) keeping the angles found but 
   reduce the size of line segment ab.  Set up the ratio: Line AB over line ab 
   = X (AC) over line ac.

4. To verify, measure the distance from point A to point C.  Compare with the 
   calculated answer.  Use the formula: Actual measurement minus Calculated 
   measurement divided by Actual to obtain the margin of error.  

Performance Assessment:

   A similar problem like part two can be used as a performance assessment. 
   The students are to answer the following question.  What is the length of 
   line AC?

Conclusion:
   
   Knowing two angles and the distance between them, you can find the distance
   of the point that completes the triangle.  This can be done by making a 
   smaller model to help calculate the answer.