Haley is standing in the base path between second and third base when she fields the ball. She is 24 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth. The numbers used is 24 and 32

Question

Haley is standing in the base path between second and third base when she fields the ball. She is 24 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth. The numbers used is 24 and 32

Answer 1

To find how far Haley needs to throw the ball, we can use the Pythagorean theorem since the field is square. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the hypotenuse.

Let's call the distance Haley needs to throw the ball "x". The distance between second base and first base is 90 feet, so we have a right triangle with sides of length 24 feet (distance from second base to Haley) and 90 feet (distance from second base to first base). Using the Pythagorean theorem:

24^2 + x^2 = 90^2
576 + x^2 = 8100
x^2 = 7524
x = sqrt(7524) ≈ 86.7

Therefore, Haley needs to throw the ball approximately 86.7 feet to reach first base.