We first approach this problem by forming a diagram. Refer to the attachment.
You might notice a right triangle forming when you connect cities A, B, and C. In this case, we'll just need the Pythagorean theorem when solving for the distance between city B and city A.
[tex]AB^{2}=BC^{2} + AC^{2}= 75^{2} + 42^{2} =7389[/tex]
[tex]AB=85.96[/tex]
ANSWER: The distance between city B and city A is 85.96 kilometers.
