If I was told to walk 43 degrees N for 20 miles but instead walked 40 degrees N for 20 miles how far off would I be from my original destination?

nice triangle, with sides 20,20 and the contained angle between them as 3°

could just use cosine law:
x^2 = 20^2+20^2-2(20)(20)cos3°
= 1.09637..
x = √1.09...
= appr 1.047 miles

or

since you have an isosceles triangle, draw and altitude to get a right-angled triangle.
base/20 = cos 1.5°
base = 20sin1.5 = .5235.
so distance apart = 2(.5235..) = 1.047 , just as above