Question

Two planes leave the airport at the same time. In one hour the plane that has flown north has traveled 400 miles. The plane that has flown southwest has traveled 250 miles. How far apart are the planes?

LAW OF COSINES
GEOMETRY

Answer 1

`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 ( √(2) )/(2) \\\\x^2=222,500+100,000\cdot √(2) \\\\x^2=2500\cdot(89+40 √(2) )\\\\`


`x=50\cdot \sqrt{89+40 √(2)} \ \ \ \Rightarrow\ \ \ x\approx603.26\ [miles]\\\\Ans.\ the\ distance\ is\ about\ 603.26\ miles`