Hideko is a pilot with a small two-seater plane. She took off from the airport and headed south toward her hometown. After flying for miles, Hideko turned the plane to the west to avoid a large storm. She remained on this course for miles before turning back to the east and continuing on to land near her hometown. How much farther did Hideko fly than she would have if she could have remained on her original course? Determine whether your answer is reasonable given the context of the problem.

Draw and label a sketch of the situation.

Find the measure of and .

Find using the Law of Sines.

Find using the Law of Sines.

Determine how much farther Hideko flew as a result of changing course.