Tom crossed a river that was 100 ft. wide by heading straight across. The river swept him down stream at an angle of 35° from straight across.

How far did he have to walk up the opposite bank to stand straight across from where he started?

35 degrees is approximately 1/10 of a circle’s circumference.

So I draw a circle centered at Tom’s starting point. Then I find 1/8 of the circle’s circumference. 1/10 is 80% of 1/8, so I then found 1/10 of the circle’s circumference.

I drew a ray through that point on the circle, marked the intersection with the other bank, and then measured the segment that represents 100 ft and the segment that represents how far Tom had to walk.

The segment that represents how far Tom had to walk is 83% as long as the segment representing the river’s width, so Tom had to walk approximately 83 feet.