An illustration shows a square with smaller squares representing baseball plates on the top left, top right, and bottom right vertices. The bottom left vertex has a pentagon that represents home plate. A stick figure is located on the top of the square and the measurement from the right vertex to the stick figure is labeled 30 feet. A dashed diagonal line runs from the stick figure to the inner right side of the square, forming the hypotenuse of a triangle. The top right side of the square forms the right angle of the triangle and is marked with a right angle symbol. The outer right side of the square is labeled 90 feet.
A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 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.
To find the distance the shortstop needs to throw the ball, we can use the Pythagorean Theorem, which states a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides of a right triangle, and c is the length of the hypotenuse.
In this case, the shortstop is 30 feet from second base and the entire field is 90 feet wide. So the length of one side of the square (a) is 90 feet. The distance from the shortstop to first base represents the hypotenuse of the right triangle.
Using the Pythagorean Theorem:
30^2 + b^2 = 90^2
900 + b^2 = 8100
b^2 = 7200
b = √7200
b = 84.9 feet
Therefore, the shortstop needs to throw the ball approximately 84.9 feet to reach first base.