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When it says direction of the trip, where is your starting point of 0 degrees? Due east, or due north, or due west?
If 0 degrees is due east then the answer is 180-arctan(53/22)
Their answer of 23 degrees is likely based on assuming that 0 degrees is due north
the direction is measured with respect to true north.
In that case the answer would be 22.54 degrees west of true north
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About 337.5 deg.
in navigation the angle is measured wrt north.
Rounded to nearest tenth, as indicated in the problem.
dpalnc is correct. For navigation, angles are measured from zero to 360 degrees clockwise from North. North is usually referred to by 360, instead of zero.
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