Question 935033: If the wind is at 14 mph out of the east, how fast can a sailboat travel in a southwest direction? ( mph )
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! the real answer is very complicated, but if we assume that the sailboat is 100% efficient (no water drag, no air drag, and the sail is 100% efficient):
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make an isoceles right triangle to model the wind acting on the sail:
hypotenuse "c" = 14 mph
angle opposite "c" = C = 90 degrees
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angle A = angle B = 45 degrees
find side "a" opposite to angle A:
note that side "a" and side "b" have the same length ...
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use the law of sines:
a/sinA = c/sinC
a = sinA * c/sinC
a = sin(45) * 14/sin(90)
a = 9.9
b = 9.9
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answer:
a = 9.9 mph
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