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Question 1005671: An arctic village maintains a circular cross-country ski trail that has a radius of 3.7 kilometers. Suppose that a skier started skiing from the position (3.7, 0) and skied clockwise for 7.5 kilometers before stopping for a rest.
Determine the ordered pair (measured in radius lengths and kilometers) on the coordinate axes that identifies the location where the skier rested.
Thank you for your time.
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! Let's see...
The circumference of the trail is C = 2(pi)r = 23.236 km.
If the skier skis clockwise 7.5 km, they have traversed .323 of the circle, or 116.2 degrees.
Subtracting 90 degrees, they are 26.2 degrees west of south, ata distance of 3.7 from the origin.
Thus their position would be (-3.7sin(26.2), -3.7cos(26.2)) km.
In radius lengths, that is just (-sin(26.2), -cos(26.2)) of them.
How's that?
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