Three baseball players are playing catch. Barry is 12 feet south of Regan and 16 feet west of Addison. How far does Regan need to throw the ball to get it to Addison?

Answer 1

To find the distance Regan needs to throw the ball to get it to Addison, we can use the Pythagorean theorem.

Let's assume that Barry is at point B, Regan is at point R, and Addison is at point A.

Since Barry is 12 feet south of Regan, we can draw a vertical line connecting B and R with a length of 12 feet.

Since Barry is 16 feet west of Addison, we can draw a horizontal line connecting B and A with a length of 16 feet.

This creates a right-angled triangle with one side measuring 12 feet and the other side measuring 16 feet.

To find the length of the hypotenuse, which is the distance Regan needs to throw the ball to get it to Addison, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

c^2 = a^2 + b^2

Let's substitute the values into the equation:

c^2 = 12^2 + 16^2
c^2 = 144 + 256
c^2 = 400

To find the value of c, we need to take the square root of 400:

c = sqrt(400)
c = 20

Therefore, Regan needs to throw the ball a distance of 20 feet to get it to Addison.