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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To find the distance the shortstop needs to throw the ball, we can use Pythagoras' theorem since we have a right triangle. The hypotenuse of the triangle represents the distance she needs to throw the ball.
The length of the right side of the square is given as 90 feet, and the measurement from the right vertex to the stick figure is given as 30 feet. Using these values, we can find the length of the hypotenuse of the triangle.
Using the Pythagorean theorem, we have:
(Length of hypotenuse)^2 = (Length of right side)^2 + (Measurement from the right vertex to the stick figure)^2
Let's substitute the given values:
(Length of hypotenuse)^2 = 90^2 + 30^2
Simplifying:
(Length of hypotenuse)^2 = 8100 + 900
(Length of hypotenuse)^2 = 9000
Taking the square root of both sides to solve for the length of the hypotenuse:
Length of hypotenuse = √9000
Rounded to the nearest tenth, the length of the hypotenuse, or the distance the shortstop needs to throw the ball, is approximately 94.9 feet.
To find the distance the shortstop needs to throw the ball, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the right triangle is formed by the 30 feet distance from second base to the shortstop (one side of the triangle) and the unknown distance the shortstop needs to throw the ball (the hypotenuse).
We can use the given information that the outer right side of the square is labeled 90 feet, and the right side of the square forms the right angle of the triangle. Therefore, we can label the other side of the triangle as 90 - 30 = 60 feet.
Applying the Pythagorean theorem, we have:
(60 feet)^2 + (30 feet)^2 = (shortstop throw distance)^2
Simplifying the equation:
3600 + 900 = (shortstop throw distance)^2
4500 = (shortstop throw distance)^2
Taking the square root of both sides of the equation:
shortstop throw distance = √4500 ≈ 67.1 feet
Therefore, the shortstop needs to throw the ball approximately 67.1 feet to make the throw to first base.
To answer this question, we need to use the information provided in the image and some geometry principles.
First, let's understand the information given in the image. We have a square representing the baseball field. The stick figure is located on the top of the square, and the measurement from the stick figure to the right vertex is labeled as 30 feet. The outer right side of the square is labeled as 90 feet.
We can see that the stick figure, representing the shortstop, is located on the right side of the field, 30 feet away from second base. To find out the distance she needs to throw the ball to first base, we need to find the length of the diagonal line connecting the stick figure to the inner right side of the square.
Since the field is square, we know that the diagonal line will represent the hypotenuse of a right-angled triangle. The other two sides of the triangle are the distance from the stick figure to the right vertex (30 feet) and the outer right side of the square (90 feet).
Using the Pythagorean theorem, we can find the length of the diagonal line (hypotenuse).
Pythagorean theorem: In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's calculate it step by step:
Step 1: Square the length of the two known sides:
30^2 = 900 (feet)
90^2 = 8100 (feet)
Step 2: Add the squares together:
900 + 8100 = 9000 (feet)
Step 3: Take the square root of the sum:
√9000 ≈ 94.8683298059
Therefore, the shortstop needs to throw the ball approximately 94.9 feet to reach first base (rounded to the nearest tenth).
Answer: 94.9 feet.