Currency Arb question, triangle, problem, matter, method

torontoanalyst

I had a question that had me calculate the arb profit given 3 currencies fx rates. This problem did not have bid/ask they just gave the fx rate.

Rather than using the triangle I solved by calculating what one of the cross rates should be.

Will that work in all cases or was it just this time?

does it matter which cross rate you check?

does this method work if we are also given bid/ask prices?