I assume you meant
City z is 80km and in the direction of 108 from city y
So, with x at (0,0)
y is at (133.8,148.6)
z is at y + (76.1,-24.7) = (209.9,123.9)
Now just apply the usual distance formula and conversion to polar form.
City y is 200km and in the direction of 048 from city x. City x is 80km and in the direction of 108 from city y. Find the distance of city z from city x and the bearing of city x from z
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