Plane Detour

Clar's Stars
Topic: Plane Geometry
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187. A pilot flying due east is forced to make a detour from her original route to avoid turbulent weather. The pilot turns 30 degrees north of east. After traveling some distance, she turns and rejoins her original route and is 1000 km away from where she took the detour. The turn back to her original route put her at a 45 degree angle to that route. How much farther did the pilot travel due to her detour? Express your answer to the nearest whole kilometer.

Video by Charles Tsai, Clara Merry, Evan Fagan, and Taran CoyneSmith.

Common Core Standards: G-SRT.6
Problem #: 
187 (2017-2018)
Problem Difficulty Level: 5 [?]