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. (1 point) How many feet?
numbers used are 32 ft and 24 ft!
To find the distance Haley needs to throw the ball, we can use the Pythagorean theorem.
The distance between second base and first base is the hypotenuse of a right triangle, with Haley standing at the base path as one of the legs. The other leg represents the distance between Haley and first base.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can substitute the given values:
(24 ft)^2 + b^2 = (32 ft)^2
576 ft^2 + b^2 = 1024 ft^2
b^2 = 1024 ft^2 - 576 ft^2
b^2 = 448 ft^2
Taking the square root of both sides:
b ≈ √448 ft
b ≈ 21.2 ft
Therefore, Haley needs to throw the ball approximately 21.2 feet to first base.