Factor out cosx: cosx(sinx-2)=0 cosx=0 or sinx-2=0 cosx=0 or sinx=2 the largest value of sinx is 1, sinx will never be 2, so cosx=0, x=π/2 or 3π/2 are the two answers.
Lets round each distance to the nearest tens place, and then add them up to get an estimate. 143 rounds down to 140, 138 rounds up to 140, and 141 rounds down to 140. So: 140 + 140 + 140 = 420 miles