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, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the distance from second base to first base represents the hypotenuse, and the distance from second base to third base represents one of the sides of the right triangle. Haley needs to throw the ball from the point where she fields it to first base.
Given that Haley is standing 24 feet from second base, and the field is square, we can determine the distance between third base and first base using the Pythagorean theorem.
Using the formula:
c² = a² + b²
where c is the hypotenuse, and a and b are the other two sides, we can substitute the values:
c² = 32² + 24²
Simplifying, we get:
c² = 1024 + 576
c² = 1600
Taking the square root of both sides to solve for c, we get:
c = √1600
c = 40 feet (rounded to the nearest tenth)
Therefore, Haley needs to throw the ball approximately 40 feet to reach first base.