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 [math]70[/math] miles, Hideko turned the plane [math]40^\circ[/math] to the west to avoid a large storm. She remained on this course for [math]95[/math] miles before turning back [math]65^\circ[/math] 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.
