Using the Pythagorean Theorem to Catch the Perfect Radio Waves!
NASA's Cassini spacecraft acquires the first detailed radar images of Saturn's moon Enceladus during a 2001 flyby.Copyright NASA http://www.nasa.gov/audience/foreducators/plantgrowth/reference/Eng_Design_5-12.html
Students learn the importance of the Pythagorean theorem as applied in radar imaging. They use a sensor unit with IRED (infrared emitting diode) to measure triangle distances and the theorem to calculate and verify distances. Student groups calibrate the sensor units to ensure accurate distance measurements. A "pretend" outdoor radar imaging model is provided to groups for sensor unit testing.
Math, science and engineering play an indisputable role in the creation of modern measuring devices. Without some of these devices, it would be extremely difficult or even impossible to measure distances due to bad weather, hostile territory or remote location. Examples devices include synthetic aperture radars (SAR) developed by electrical engineers. SAR systems use radio waves and echoes to measure slant range (distance from radar to target) and ground range (horizontal or ground distance from radar to target). SAR technology provides structural terrain information for mineral exploration, reconnaissance and targeting information for military operations, and oil spill boundaries on water to help with clean-up. A right triangular model can be used to illustrate the distance relationships formed from the radar, target and targets altitude. Similar to SARs, we can use the geometric concept of the Pythagorean theorem to calculate the distances in any right triangle model. Without an accurate measurement of distance, SARs would not be able to produce high-resolution images of remote locations.
After this activity, students should be able to:
- Demonstrate a basic understanding of a synthetic aperture radar (SAR) system.
- Formulate a tabular and graphical model that describes the relationship between variables.
- Use the Pythagorean theorem to calculate side lengths of right triangles.