Final answer:
The boat has traveled a distance of 50 miles and is located 40 miles east and 30 miles north from the start point.
Step-by-step explanation:
To find the distance traveled by the boat, we can use the Pythagorean theorem. The boat sails 30 miles north and then 40 miles east, forming a right triangle. The distance traveled by the boat is the hypotenuse of this triangle.
Using the Pythagorean theorem, we can calculate the distance:
Distance = sqrt((30^2) + (40^2))
Distance = sqrt(900 + 1600)
Distance = sqrt(2500)
Distance = 50 miles
To find the location of the boat from the start point, we can use the concept of displacement. Displacement is a vector that represents the change in position of an object.
In this case, the boat has traveled 30 miles north and 40 miles east, so its displacement would be (40,30). This means the boat is 40 miles east and 30 miles north from the start point.