Consecutive bases of a square shaped baseball diamond are 90 feet apart .Find to the nearest tength of a foot the distance from first base diagonally across the diamond to third base
d^2 = 90^2 + 90^2
etc
To find the distance from first base diagonally across the diamond to third base, 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 distance between consecutive bases on the square-shaped baseball diamond is given as 90 feet. So, the length of one side of the square is also 90 feet.
Let's label the distance from the first base to third base as "d" (the hypotenuse). The distance from first base to second base and from second base to third base are both equal to 90 feet (the other two sides).
Using the Pythagorean theorem, we can write the equation as:
d^2 = 90^2 + 90^2
Simplifying:
d^2 = 8100 + 8100
d^2 = 16200
Taking the square root of both sides to find the distance "d":
d = √16200
Calculating this on a calculator, we find:
d ≈ 127.28 feet
Rounded to the nearest tenth of a foot, the distance from first base diagonally across to third base is approximately 127.3 feet.