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Area of Sectors and Segments

Area of parts of a circle.

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Watch Out for the Weather!

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

In the nose of an airplane there is a weather radar that sweeps backwards and forwards, like a windshield wiper, to map clouds and storms that could pose problems. How much time do pilots have to use this information to protect their passengers?

Why It Matters

What the pilot is looking at is a sector of the airspace in front of him, as shown in the image above. The dashed green line to the right of center is the current position of the radar sweep. Radars display an image showing the position of the airplane, the presence of clouds that reflected the radar beam, and measurements regarding the plane's trajectory, including its current speed and distance from the radar horizon.

Credit: Larry Aaron
Source: http://commons.wikimedia.org/wiki/File:The_navigation_officer_on_a_Boeing_707_aircraft,_leaving_Rhein_Main_Air_Base,_Germany,_plots_a_course_using_a_laptop_computer_in_connection_with_the_Joint_Surveillance_Target_Attack_Radar_System_(J-STARS)_960219-A-KF633-004.jpg
License: CC BY-NC 3.0

The airplane in the first illustration will reach the upper edge of the screen that we can see in 11 minutes. If the pilot is going to respond to what he sees, he does not have a lot of time in which to do it!

See all about aircraft weather radar for yourself: http://www.gapan.org/ruth-documents/study-papers/Weather%20Radar.pdf

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Given that the scan is 58 degrees, how much of the sky can the pilot see when he looks at the weather radar?

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