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) feet
To find the distance Haley needs to throw the ball, we can use the Pythagorean theorem.
Let x be the distance she needs to throw the ball.
According to the problem, she is standing 24 feet from second base. Let's call this distance y.
Based on the problem, we can see that she is forming a right triangle with the distance she needs to throw the ball as the hypotenuse (x) and the distance from second base to first base as one of the legs (24 feet). So, we have the equation:
x^2 = 24^2 + y^2
Now, from the problem, we can see that the field is square, so the distance from second base to first base would also be 24 feet. So, y = 24 feet.
Now, let's substitute this value back into our equation and solve for x:
x^2 = 24^2 + 24^2
x^2 = 576 + 576
x^2 = 1152
To find x, we need to take the square root of both sides:
x = √(1152)
x ≈ 33.9
Therefore, Haley needs to throw the ball approximately 33.9 feet to first base.