Miguel is driving his motor boat across the river. the speed of the boat in still water is 14 mi/h. the river flows directly south at 2 mi/h. if miguel heads directly west, what are the boats resultant speed and direction? diagram is not drawn to scale.

Refer to the diagram shown below.

The resultant speed of the boar is v, and its direction is θ degrees south of west.

Use the Pythagorean Theorem to calculate v.
v² = 14² + 2² = 200
v = √(200) = 14.1 mi/h

By definition,
tan θ = 2/14 = 0.1429
θ = tan⁻¹ 0.1429 = 8°

14.1 mi/h; 8° south of west.