# math

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A vessel sails 32 miles S 45 degrees E. How far south has it sailed?

The wording of it confuses me.

• math -

Total distance travelled is 32 miles. The south component of the displacement is is 32 cos 45 = 22.63 miles. On a map, that is how much the southern coordinate changes.

There is an eastern displacement of the same amount, 32 sin 45 = 22.63 miles.

The hypotenuse, which is the displacement vector magnitude, is 45 miles

• math (correction) -

The hypotenuse, which is the displacement vector magnitude, is 32 miles

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