<PRE><B>Question 742668</B>
you walk 4 miles at 30° and then 2 miles at 135°. what is the distance of your location from the starting point
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Draw the picture on a coordinate system.
Label the triangle ABC where A is the origin, AB is the 4 mile length,
BC is the 135 degree line, CA is the distance from origin to final position.
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Sketch a vertical line thru B to the x-axis at point X.
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Angle ABX has to be 60 degrees.
Angle ABC has to be 180-60-45 = 75 degrees.
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Use the Law of Cosines to solve for  CA.
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CA^2 = 4^2 + 2^2 - 2*4*2cos(75) = 17.929
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CA = 4.23 miles
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Cheers,
Stan H.
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