chris215
  • chris215
An airplane leaves an airport and flies due west 150 miles and then 170 miles in the direction S 49.17°W. How far is the plane from the airport (round to the nearest mile)?
Mathematics
chestercat
  • chestercat
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chris215
  • chris215
|dw:1434130266939:dw|
chris215
  • chris215
i know that 90 + 49.17 = 139.17
chris215
  • chris215
now do I use c^2=a^2+b^2?

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anonymous
  • anonymous
90 + 49.17
chris215
  • chris215
yeah is that all i need to do?
anonymous
  • anonymous
|dw:1434142811182:dw|
chris215
  • chris215
= 150^2 + 170^2 - 2(150)(170cos)(139.17) = 226 miles
anonymous
  • anonymous
angle as i have shown in the figure angle is (180-49.17)
anonymous
  • anonymous
\[\cos (180-49.17)=-\cos 49.17\]
anonymous
  • anonymous
\[- \cos 49.17=\frac{ 150^2+170^2-OB^2 }{ 2*150*170 }\]
anonymous
  • anonymous
\[5100 *(-\cos 49.17)=22500+28900-OB^2\]

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