Your pilot watch just has the C and D scales on it, no trig scales. That means that unless you've memorized the sines of some reference angles, you're stuck. That's a pity, because the slide rule would be a great, reliable, fast way to do that calculation. Chained multiplications and divisions, with no addition or subtraction, is where they shine.

There is a Japanese company which makes pocket-sized circular scientific slide rules which would be great for that use, and they're quite reasonably priced. Their number 270 (see here) would do the job, and it's only about $20. Unfortunately, they want 10,000 yen to ship to the U.S. That's about $100, so I haven't bought any of their $20 slide rules yet. Maybe some day I'll stop in Japan and find one in an airport gift shop.