https://file.aiquickdraw.com/mathbot/file/1730230648278gapiygzi.jpg

To solve for the total distance the airplane flew, we need to examine each leg of its flight path. Let's break down the details from the image and use trigonometry to solve it:

### Step-by-Step Solution

1. **Leg 1: Original Airport to Turning Point**  
   - The airplane flies in a direction of \( 83^\circ \) from the original airport.
   
2. **Leg 2: Turning Point to New Airport**  
   - It then returns 210 km due north of its starting point, forming a right triangle.  
   - This leg of the trip is directly north.

3. **Leg 3: New Airport to Turning Point**  
   - The plane then flies to the new airport, 280° from the north, back to the original location.
   


A reconnaissance airplane leaves its airport on the east coast of country A and flies in a direction of 83°. Because of bad weather, it returns to another airport 210 km due north of its home base. To get to the new airport, it flies in a direction of 280°. What is the total distance that the airplane flew?

This problem involves using trigonometry to calculate the total distance flown by an airplane taking two legs of a journey at specified angles. It includes key mathematical concepts such as the Law of Cosines and the Pythagorean Theorem, making it suitable for students in Grades 10-12.

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