Question

a fisherman sailed farther to sea to find a good catch. He sailed directly east for 55.3 km. Then he sailed Northeast for 25.0 km. From that point. He continued sailing toward a straight path and found himself 200 km. East from his original posisition.

Answer 1

If you draw an image of the fisherman's adventure, the problem becomes way more easier:

So, we can write an equation using the horizontal and vertical projections of his path:

$$200=55.3+25\space\text{sin}\space 45^\circ+x\space\text{sin}\space\alpha,$$

in vertical direction the fisherman's displacement is 0:

$$0=25\space\text{cos}\space45^\circ+x\space\text{cos}\alpha.$$

Solve this system and get that

$$x=128.25\text{ km}, \alpha=97.92^\circ.$$