A shortstop is standing in the base path between second and third base when she fields the ball. She is 25 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.
Using the Pythagorean theorem, we can find the distance she needs to throw the ball:
distance = √(25^2 + 90^2)
distance = √(625 + 8100)
distance = √8725
distance ≈ 93.4 feet
Therefore, she needs to throw the ball approximately 93.4 feet.
To calculate the distance the shortstop needs to throw the ball, we will use the Pythagorean theorem.
The distance from second base to first base can be considered as the hypotenuse of a right-angled triangle. The two sides of the triangle are the distance from the shortstop to second base and the distance from the shortstop to first base.
Using the Pythagorean theorem, we can solve for the length of the hypotenuse:
hypotenuse² = side₁² + side₂²
Let's substitute the given values into the equation:
hypotenuse² = 25² + 90²
hypotenuse² = 625 + 8100
hypotenuse² = 8725
To find the length of the hypotenuse, we take the square root of both sides:
hypotenuse = √8725
hypotenuse ≈ 93.4
Rounding to the nearest tenth, the shortstop needs to throw the ball approximately 93.4 feet to make it to first base.
To solve this problem, we need to use the Pythagorean theorem since we are dealing with a right triangle. The distance from the shortstop to second base forms one side of the right triangle, and the distance from the shortstop to first base forms the other side. The distance between second and first base is the hypotenuse.
Let's name the distance from the shortstop to first base as "x". We already know that the distance from the shortstop to second base is 25 feet, which we'll call "y".
Using the Pythagorean theorem, we have:
x^2 = y^2 + 25^2
To find the value of x, we substitute the given value of y and solve for x.
x^2 = 25^2 + 25^2
x^2 = 625 + 625
x^2 = 1250
To find the value of x, we take the square root of both sides:
x = √1250
x ≈ 35.4 feet
Therefore, the shortstop needs to throw the ball approximately 35.4 feet to reach first base.
bot r u sure
I apologize for the error in my previous response. You are correct, and I made a mistake in calculating the distance. I apologize for any confusion caused.
To solve this problem correctly, let's use the Pythagorean theorem:
Distance^2 = 25^2 + 90^2
Distance^2 = 625 + 8100
Distance^2 = 8725
Taking the square root of both sides, we can find the distance:
Distance ≈ √8725
Distance ≈ 93.4 feet
So, the correct answer is approximately 93.4 feet. Thank you for pointing out the mistake, and I apologize for any confusion caused.