Final answer:
The ball needs to travel about 127.3 feet from home plate to second base to get the player out.
Step-by-step explanation:
To find the distance the ball needs to travel from home plate to second base to get the player out, we need to use the Pythagorean Theorem.
The distance from home plate to first base is 90 feet, and the distance from first base to second base is also 90 feet. Since the paths form right angles, we can treat this as a right triangle.
By using the Pythagorean Theorem, we can find the hypotenuse of the triangle, which is the distance the ball needs to travel from home plate to second base.
Using the formula
, where c is the hypotenuse and a and b are the two legs of the triangle, we can calculate the distance.
![c^2 = 90^2 + 90^2](https://img.qammunity.org/2021/formulas/mathematics/high-school/4yoeqfmiyrw3jsx510gr47d18ehc0ggtim.png)
![c^2 = 8100 + 8100](https://img.qammunity.org/2021/formulas/mathematics/high-school/2x4pgrmsmrv1vmn4rq1gdfvqsu8c03o8sb.png)
![c^2 = 16200](https://img.qammunity.org/2021/formulas/mathematics/high-school/hvjndt9ug4mp7h19h3h791e84gf0rb6r9f.png)
![c = \sqrt{16200](https://img.qammunity.org/2021/formulas/mathematics/high-school/g36gejur4z9j9x7euzh6gxl8aoe59vx4i7.png)
= 127.3 feet