Use the image to answer the question.
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.
(1 point)
feet
The distance she needs to throw the ball is equal to the length of the dashed diagonal line from the stick figure to the inner right side of the square.
From the given information, we know that the length of the right side of the square is 90 feet. The measurement from the right vertex to the stick figure is labeled 30 feet, and we can see that this forms the hypotenuse of a right triangle.
Using the Pythagorean theorem, we can calculate the length of the dashed diagonal line:
c^2 = a^2 + b^2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides of the triangle.
In this case, a = 30 feet and b = 90 feet.
c^2 = 30^2 + 90^2
c^2 = 900 + 8100
c^2 = 9000
Taking the square root of both sides to solve for c:
c = √9000
c ≈ 94.8683
Therefore, the shortstop needs to throw the ball approximately 94.9 feet.