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
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The distance the shortstop needs to throw the ball can be calculated using the Pythagorean theorem, which states that for a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the distance from the shortstop to second base is 30 feet and the distance from the shortstop to first base (which we need to calculate) is the hypotenuse. The distance from second base to first base is the side length of the square, which is 90 feet.
Using the Pythagorean theorem: (30^2 + 90^2) = c^2
(900 + 8100) = c^2
9000 = c^2
c = √9000
c ≈ 94.9 feet
So, the shortstop needs to throw the ball approximately 94.9 feet to first base.