360 miles would be the hypotenuse of our right triangle. 7°50' would be our angle A. Since we are looking for the base of this triangle. We will be using the cosine function.

cos= \frac{adjacent}{hypotenuse}
First, we need to derive the formula for the adjacent or the base of the triangle since that is the unknown. The formula would be:
adjacent= hypotenuse(cosA)
Substituting the given,
adjacent= 360 miles(cos7degrees50minutes)
               = 356.64 miles

Subtracting the answer from the needed 1,400 miles we get 1,043.36 miles.