to avoid a large shallow reef, a ship is set a course from point a and traveled 25 miles east to point b. the ship then turned a traveled 35 miles south to point c.if the ship could have gone in a straight line from point a to point c. how many miles could it have saved?
To find out how many miles the ship could have saved by going in a straight line from point A to point C, we need to calculate the distance between point A and point C, and then compare it to the actual distance traveled by the ship.
First, let's visualize the situation.
- Point A: Starting point.
- Point B: Reached by traveling 25 miles east from Point A.
- Point C: Reached by turning and traveling 35 miles south from Point B.
Now, we can calculate the distances:
1. Distance from Point A to Point B: The ship traveled 25 miles east, so the distance is 25 miles.
2. Distance from Point B to Point C: The ship traveled 35 miles south.
Since the ship could have gone in a straight line from Point A to Point C, we can create a right-angled triangle with the lines AB, BC, and AC as the hypotenuse. The distance BC equals the vertical leg, and the distance AB equals the horizontal leg.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the hypotenuse (distance AC):
AB^2 + BC^2 = AC^2
Since AB is 25 miles and BC is 35 miles:
25^2 + 35^2 = AC^2
625 + 1225 = AC^2
1850 = AC^2
Finding the square root of 1850:
AC ≈ 43 miles (rounded to the nearest whole number)
So, the ship could have saved approximately 43 miles if it went in a straight line from Point A to Point C.