Shortstop is standing in the base path between the second and third base when fields the ball. She is 30 feet from second base and needs to make the throughout first base assuming the For Square how far does she need to throw the ball around your answer to the nearest tenth
To answer this question, we need to determine the distance she needs to throw the ball in order to reach first base.
We can use the Pythagorean theorem to find the diagonal distance from second base to first base, which represents the distance the shortstop needs to throw the ball.
Using the formula: c^2 = a^2 + b^2, where c is the hypotenuse (the distance to find), and a and b are the other two sides of the right triangle (30 feet and 90 feet).
c^2 = 30^2 + 90^2
c^2 = 900 + 8100
c^2 = 9000
Taking the square root of both sides:
c = √9000
c ≈ 94.9
Therefore, the shortstop needs to throw the ball approximately 94.9 feet to reach first base.
Rounded to the nearest tenth, the answer is approximately 94.9 feet.
To determine the distance the shortstop needs to throw the ball, we can use the Pythagorean Theorem. We can form a right triangle with the shortstop at the right angle, the distance from second base to first base as the hypotenuse, and the distance from the shortstop to second base as one of the legs.
Let's calculate it step-by-step:
1. Find the length of the hypotenuse (distance from second base to first base):
According to the problem, the distance between second and third base is 30 feet. Since the bases form a square, this means the distance from second base to first base is also 30 feet.
2. Find the length of the leg (distance from the shortstop to second base):
This is given as 30 feet in the problem.
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. So, we can use the formula:
c² = a² + b², where c is the length of the hypotenuse and a and b are the lengths of the legs.
Plugging in the values:
c² = 30² + 30²
c² = 900 + 900
c² = 1800
4. Calculate the length of the hypotenuse (distance shortstop needs to throw):
Taking the square root of both sides to solve for c:
c = √1800
c ≈ 42.4 feet
Therefore, the shortstop needs to throw the ball around 42.4 feet to reach first base.
To determine the distance the shortstop needs to throw the ball to first base, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square 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 path from the shortstop to the first baseman forms a right triangle, with one side being the distance between the shortstop and second base (30 feet), and the other side being the distance between second base and first base (90 feet, assuming a square infield).
Using the Pythagorean theorem, we can calculate the distance the shortstop needs to throw the ball:
Distance^2 = 30^2 + 90^2
Distance^2 = 900 + 8100
Distance^2 = 9000
Distance = √9000
Distance ≈ 94.87 feet
Therefore, the shortstop needs to throw the ball around 94.9 feet to first base, rounding to the nearest tenth.