The route followed by a hiker consists of three displacement vectors A, B , and

Question

The route followed by a hiker consists of three displacement vectors A, B , and C. Vector A is along a measured trail and is 1550 m in a direction 28.0° north of east. Vector B is not along a measured trail, but the hiker uses a compass and knows that the direction is 41.0° east of south. Similarly, the direction of vector C is 26.0° north of west. The hiker ends up back where she started, so the resultant displacement is zero, or A+B+C= 0. Find the magnitudes of vector B and vector C.

I don't know how to find the magnitude of two vectors with only the magnitude of one.

Explanation / Answer

I think the easiest method (and hence the one less likely to make mistakes) is to calculate all the internal angles of the triangle using basic geometry, then use the Law of Sines. The angles are (where a=angle opposite vector A etc) b = 27+27 = 54 deg c = 41+(90-27) = 104 deg a = 180-b-c = 22 deg Magnitude of vector B = 1550*sin(54)/sin(22) = 3347.4m Magnitude of vector C = 1550*sin(104)/sin(22) = 4014.8m

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