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please answer this geometry question

Mathematics
Tutor: None Selected Time limit: 1 Day

Apr 10th, 2015

The east component of the plane's speed is 600sin55 = 491.49 mi/h

The north component of the plane's speed is 600cos55 = 344.15 mi/h

The east crosswind adds 50 mi/h to the plane's east component speed: 491.49+50 = 541.49 mi/h

The north speed component remains unchanged.

Then, the plane's actual speed is

sqrt(344.15^2 + 541.49^2) = 641.6 mi/h

the direction is found by

tan^-1(541.49/344.15) = 58 degrees

So, the actual direction is N58E

Apr 10th, 2015

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