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. Explain how the answer is 94.9
To find how far 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, we can consider the distance from the shortstop to second base as one side of the right triangle, and the distance from the shortstop to first base as the other side. The distance from second base to first base will be the hypotenuse.
The shortstop is 30 feet from second base, and we need to find the distance from second base to first base. We can let this distance be represented by x.
Using the Pythagorean Theorem:
x^2 = 30^2 + 30^2
x^2 = 900 + 900
x^2 = 1800
Taking the square root of both sides:
x = √1800 ≈ 42.4
So, the shortstop needs to throw the ball approximately 42.4 feet from second base to first base.
Rounded to the nearest tenth, the shortstop needs to throw the ball 42.4 feet to first base, which would be approximately 42.4 rounded to the nearest tenth.
Hence, the answer is 42.4 feet.
no dumbo, the answer is 94.9. Explain how the answer is 94.9
Apologies for the incorrect explanation earlier. Let's recalculate the correct answer.
To find how far 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, we can consider the distance from the shortstop to second base as one side of the right triangle, and the distance from the shortstop to first base as the other side. The distance from second base to first base will be the hypotenuse.
The shortstop is 30 feet from second base, and we need to find the distance from second base to first base. We can let this distance be represented by x.
Using the Pythagorean Theorem:
x^2 = 30^2 + 90^2
x^2 = 900 + 8100
x^2 = 9000
Taking the square root of both sides:
x = √9000 ≈ 94.9
So, the shortstop needs to throw the ball approximately 94.9 feet from second base to first base.
Hence, the answer is indeed 94.9 feet.
To find the distance the shortstop needs to throw the ball, we can use the Pythagorean Theorem, which 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 distance from the shortstop to second base is 30 feet, and we need to find the distance from the shortstop to first base.
Let's consider this as a right triangle, where the distance between second and third base forms the base, and the distance between the shortstop and first base forms the height. The distance the shortstop needs to throw the ball will be the hypotenuse of this triangle.
Using the Pythagorean Theorem, we can calculate the hypotenuse:
c² = a² + b²,
where c is the hypotenuse, a is the distance from the shortstop to second base (30 ft), and b is the distance from the shortstop to first base (unknown).
Plugging in the values:
c² = 30² + b²,
c² = 900 + b².
To find the square root of both sides, we have:
√(c²) = √(900 + b²),
c = √(900 + b²).
The distance needed to throw the ball is the value of c. However, we don't know b yet.
We can solve for b by realizing that in a square field, the distance between second and third base is the same as the distance between home plate and first base. The bases are equal in length, so if we find the distance between second base and first base, we can use that value as the value of b.
Assuming a square field, the distance between second and third base is 90 feet, which means the distance between second base and first base is also 90 feet. Therefore, b = 90 ft.
Now we can calculate c:
c = √(900 + b²),
c = √(900 + 90²),
c = √(900 + 8100),
c = √9000,
c ≈ 94.9 feet.
Therefore, the shortstop needs to throw the ball approximately 94.9 feet to first base (rounded to the nearest tenth).