[tex]a^2=b^2+c^2-2\cdot b\cdot c\cdot cos \alpha \\---------------\\\\x^2=250^2+400^2-2\cdot250\cdot400\cdot cos135^0\\\\x^2=62,500+160,000-200,000\cdot cos(180^0-45^0)\\\\x^2=222,500-200,000\cdot(-cos45^0)\\\\x^2=222,500-200,000\cdot \frac{ \sqrt{2} }{2} \\\\x^2=222,500+100,000\cdot \sqrt{2} \\\\x^2=2500\cdot(89+40 \sqrt{2} )\\\\[/tex]
[tex]x=50\cdot \sqrt{89+40 \sqrt{2}} \ \ \ \Rightarrow\ \ \ x\approx603.26\ [miles]\\\\Ans.\ the\ distance\ is\ about\ 603.26\ miles[/tex]
