SOLUTION: An airplane travels 1000 miles on a bearing of 210�. Then, it changes to a bearing 270� and travels 500 miles. How far is the airplane from the starting point? https://cds.flips

Question 1062333: An airplane travels 1000 miles on a bearing of 210�. Then, it changes to a bearing 270� and travels 500 miles. How far is the airplane from the starting point?
https://cds.flipswitch.com/tools/asset/media/573164
What is the measure of ∠ABC?
m∠ABC= __________�
Which of the following laws would help you to find the length of AC�?
Law of Cosines
Law of Sines

How far is the airplane from the starting point?
AC≈ __________ miles
Enter your answer as the number rounded to the nearest hundredth that correctly fills in the blank in the previous sentence.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Angle ABC is 120 degrees. Parallel lines perpendicular to the new course are cut by a transversal that was the first leg of the trip. That course is angled 30 degrees to the 180-360 degree line. The other alternate interior angle is therefore 30 degrees, and that is added to the 90 degrees from due north that the plane is now flying.
Law of Cosines:
c^2=a^2+b^2-2ab cos C
c^2=1000^2+500^2-2*1000*500*cos 120
=1750000.
c=1322.88 miles
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