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
Skip to navigation
Based on the information given in the image, the shortstop needs to throw the ball from second base to first base. We can use the Pythagorean theorem to find the distance she needs to throw.
The bottom right vertex of the square represents first base, and the top left vertex represents second base. According to the image, the diagonal line from the stick figure (representing the shortstop) to the inner right side of the square is the hypotenuse of a right triangle.
The length from the right vertex to the stick figure is labeled as 30 feet, and the outer right side of the square is labeled as 90 feet. This means that the length from the right vertex to the inner right side of the square (which is also the length of the square) is 90 - 30 = 60 feet.
Using the Pythagorean theorem, we can calculate the length of the hypotenuse:
c^2 = a^2 + b^2
c^2 = (30)^2 + (60)^2
c^2 = 900 + 3600
c^2 = 4500
c = √4500
c ≈ 67.1 feet
Therefore, the shortstop needs to throw the ball approximately 67.1 feet to reach first base.
Are you sure?
bot, are you sure?
To determine the distance the shortstop needs to throw the ball, we need to use the information provided in the image. Let's break down the process step by step:
1. Identify the relevant distances: According to the image, the measurement from the right vertex to the stick figure is labeled as 30 feet. Additionally, the outer right side of the square is labeled as 90 feet.
2. Understand the geometry: The shortstop needs to throw the ball from second base to first base. We can form a right triangle with the distance from the shortstop to second base as one of the legs, and the distance from second base to first base as the other leg. The hypotenuse of this triangle will be the distance the shortstop needs to throw the ball.
3. Apply the Pythagorean theorem: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can use the Pythagorean theorem to find the length of the hypotenuse (the distance the shortstop needs to throw the ball):
Hypotenuse^2 = 30^2 + (90 - 30)^2
4. Calculate the distance: Using the formula above, we can calculate the length of the hypotenuse:
Hypotenuse^2 = 900 + 3600
Hypotenuse^2 = 4500
Taking the square root of both sides:
Hypotenuse = √4500
Hypotenuse ≈ 67.1 feet
So, the shortstop needs to throw the ball approximately 67.1 feet to reach first base.