Question

To avoid a large, shallow reef, a ship set a course from point A and traveled 21 miles east to point B. The ship then turned and traveled 30 miles south to point C. If the ship could have traveled in a straight line from point A to point C, about how many miles could it have saved?

Answer 1

The ship could have saved approximately 36.61 miles by traveling in a straight line from point A to point C.

Step-by-step explanation:

To find how many miles the ship could have saved by traveling in a straight line from point A to point C, we need to calculate the distance between A and C using the given distances and directions. We can use vector addition to find the displacement between A and C.

First, we calculate the east-west component of the displacement. From point A to point B, the ship travels east for 21 miles. Then, from point B to point C, the ship travels south for 30 miles. Therefore, the east-west component of the displacement is 21 miles.

Next, we calculate the north-south component of the displacement. From point A to point B, the ship does not travel north or south, so the north-south component is 0 miles. From point B to point C, the ship travels south for 30 miles. Therefore, the north-south component of the displacement is -30 miles.

Using the Pythagorean theorem, we can find the magnitude of the displacement:

|displacement| = sqrt((east-west component)^2 + (north-south component)^2)

|displacement| = sqrt((21)^2 + (-30)^2)

|displacement| = sqrt(441 + 900)

|displacement| = sqrt(1341)

|displacement| ≈ 36.61 miles

Therefore, the ship could have saved approximately 36.61 miles by traveling in a straight line from point A to point C.

Answer 2

C I think or A not sure