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Activity (Hands-On)Grades 6 - 8

The Invisible Radar Triangle: Similarity & Scaling for Models

A photo shows an airplane flying over the Lockheed Martin TPS-79 mobile surveillance and air traffic control radar system, a 30-foot high piece of equipment mounted on tripod legs with an arc-shaped satellite dish panel.An example air traffic control radar system used by the U.S. Air Force.

Students learn about radar imaging and its various military and civilian applications that include recognition and detection of human-made targets, and the monitoring of space, deforestation and oil spills. They learn how the concepts of similarity and scaling are used in radar imaging to create three-dimensional models of various targets. Students apply the critical attributes of similar figures to create scale models of a radar imaging scenario using infrared range sensors (to emulate radar functions) and toy airplanes (to emulate targets). They use technology tools to measure angles and distances, and relate the concept of similar figures to real-world applications.

Engineers apply their understanding of math and science to the design of radars that transmit radio waves to detect objects, such as aircraft and terrain, by measuring distances between objects and the radar. To continue improving existing radar imaging techniques, engineers have developed radar imaging simulators. A radar imaging simulator uses a three-dimensional model of the target being studied to generate radar images and adjust parameters until the desired image quality is achieved. Similarity and scaling are used to create three-dimensional scale models of targets. In radar imaging, the radar, target and a point of reference on the ground form a right triangle that is used to calculate distances, and detect and identify targets. Attributes of similar figures are used to create scale models of this scenario. Ratios and proportions of corresponding sides are used to test the proportionality of scale models and calculate distances.

After this activity, students should be able to:

  • Use critical attributes of similar figures to determine if two figures are similar or not.
  • Find the measure of an angle in a triangle when given the measure of the other two angles.
  • Explain how technology is used to measure angles and distances.
  • Relate the hands-on activity to real-world applications in radar imaging.

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