After asking my professor about this question I was told that I had the quadrant

Question

After asking my professor about this question I was told that I had the quadrant correct but I did not have my answer between -180 and 180 degrees. Seeking help for part "B" of this question.

Oasis B is 8.0 km due east of oasis A. Starting from oasis A, a camel walks 21 km in a direction 15.0° south of east and then walks 32 km due north. If it is to then walk directly to B, (a) how far and (b) in what direction (relative to the positive x-axis within the range (-180° 180°]) should it walk? A dB UnitsT km (a) Number28.36 UnitsT (degrees) (b) NumberTT 244.34

Explanation / Answer

d1 = 21*(cos(15 deg) i - sin(15 deg) j ) <----------- i = unit vector along EAST, j = along NORTH

d2 = 32 j

So, d = d1 + d2

= 21*cos(15 deg) i + (32 - 21*sin(15 deg)) j

= 20.3 i + 26.6 j

Let the final displacement be d3

So, 8 i = (20.3 i + 26.6 j) + d3

So, d3 = -12.3 i - 26.6 j

So, magnitude of displacement = sqrt( 26.6^2 + 12.3^2 )

= 29.3 km

direction = 180 + atan(26.6/12.3)

= 180 + 65.2

= 245.2 deg = -(360 - 245.2) = -114.8 deg <------- answer

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