# geometry

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A cross country race course on flat ground has runners heading from point A for 3.5 km on a bearing of 047degT to point B. From point B they turn and run for 2.8 km on a bearing of 342degT to point C. They then run back to point A.

Determine the Distance from C back to A.

• geometry -

they run on a heading, not a bearing.

Starting at (0,0)
3.5 at 47° = (2.56,2.39)
2.8 at 342° = (-0.87,2.66)

Add them together to see that C is at (1.49,5.05)

CA = √(1.49^2+5.05^2) = 5.27

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