A boat is traveling east across a river that is 112 meters wide at 8 meters per second

This is the concept of application of the Pythagorean theorem. The resultant speed of the motorboat which is crossing the river that has a northward current of 5 m/s at a speed of 8 m/s will be given by:

c^2=a^2+b^2

c^2=8^2+5^2

c^2=64+25

c^2=89

c=sqrt89

c=9.4 m/s