two boats leave at the same time. one sails south and for a distance of 20 miles and finds itself 25 miles from the other boat which has sailed west how far has the other boat traveled?
x^2 + 20^2 = 25^2
x = 15
(this is a 3,4,5 right triangle)
To find out how far the other boat has traveled, we can use the Pythagorean theorem, which states:
c^2 = a^2 + b^2
where c is the hypotenuse (in this case, the distance between the two boats), and a and b are the two legs of the right triangle formed by the boats' positions.
In this scenario, one boat has sailed 20 miles south (leg a), and the other boat has sailed 25 miles west (leg b). So, we can substitute these values into the equation:
c^2 = 20^2 + 25^2
c^2 = 400 + 625
c^2 = 1025
To find c, we need to take the square root of both sides:
c ≈ √1025
Using a calculator, we find that c is approximately equal to 32.02 miles.
Therefore, the other boat has traveled approximately 32.02 miles.