A professional baseball diamond is a square. The distance from base to base is 90 ft. To the nearest foot, how far does a catcher standing at home plate throw the ball across the diagonal of the square to second base?
D^2 = 90^2 + 90^2
= 8100+8100
= 16200
D =√16200 = 127 ft , to the nearest foot
Ah, the good old baseball diamond - where "diamond" is just a fancy term for "square with fancy corners." Now, if a catcher wants to show off their arm by throwing the ball diagonally to second base, we're talking Pythagoras here!
By channeling our inner Pythagoras, we can use the formula a^2 + b^2 = c^2 to find the diagonal. In this case, both sides of the square are 90 feet, so we have 90^2 + 90^2 = c^2.
Doing some mathematical magic, 90^2 is 8100, multiplied by 2 is 16200. Take the square root of that total, and we get √16200, which is approximately 127.279 feet.
However, since we're looking for the answer to the nearest foot, let's go ahead and round it up to a nice and friendly 127 feet.
So, there you have it! A catcher standing at home plate throws the ball approximately 127 feet diagonally to second base. Don't worry, catchers are used to throwing long distances - they have to work on their throwing arms!
To find the distance from home plate to second base, we can use the Pythagorean theorem, as the baseball diamond forms a right triangle.
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 bases form the two sides of the right triangle, and the diagonal across the square is the hypotenuse.
The distance from base to base is given as 90 ft. Therefore, the two sides of the triangle are also 90 ft.
Using the Pythagorean theorem, we can calculate the length of the diagonal (hypotenuse).
Diagonal^2 = Base^2 + Base^2
Diagonal^2 = 90^2 + 90^2
Diagonal^2 = 8100 + 8100
Diagonal^2 = 16200
To find the length of the diagonal, we take the square root of both sides:
Diagonal = √16200
Diagonal ≈ 127.279 ft
Rounding to the nearest foot, the catcher standing at home plate throws the ball approximately 127 feet across the diagonal to second base.
To find the distance from home plate to second base, we can calculate the length of the diagonal of the square baseball diamond.
The baseball diamond being a square means that all four sides are of equal length. Given that the distance from base to base is 90 ft, the length of each side of the square is 90 ft.
To find the length of the diagonal, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the two sides are the lengths of the square's sides.
Let's calculate the diagonal length:
Using the Pythagorean theorem:
Diagonal^2 = Side^2 + Side^2
Diagonal^2 = 90^2 + 90^2
Diagonal^2 = 8100 + 8100
Diagonal^2 = 16200
Taking the square root of both sides:
Diagonal ≈ √16200
Diagonal ≈ 127.28 ft
Rounded to the nearest foot, the distance from home plate to second base (the length of the diagonal) is approximately 127 feet.