A softball diamond is a square with sides of 60 feet long. How far is home plate to second base? Round to the nearest tenth if necessary.
60
Home plate, first base, and second base form a right-angled triangle, with home plate to second as the hypotenuse.
Call that distance h
then h^2 = 60^2 + 60^2
etc.
To calculate the distance from home plate to second base on a softball diamond, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 lengths of the other two sides.
In this case, the distance from home plate to first base and from home plate to second base form the two sides of the triangle, and the distance from first base to second base is the hypotenuse.
Let's call the distance from home plate to second base "h". According to the Pythagorean theorem, we have the equation:
h^2 = (60^2) + (60^2)
To calculate h, we need to square the lengths of both sides of the triangle, add them together, and then take the square root of the sum.
Let's calculate it:
h^2 = (60^2) + (60^2)
h^2 = 3600 + 3600
h^2 = 7200
h ≈ √7200
h ≈ 84.85
Therefore, the distance from home plate to second base on a softball diamond is approximately 84.85 feet, rounded to the nearest tenth.
To find the distance from home plate to second base, we can use the Pythagorean theorem since home plate, first base, and second base form a right-angled triangle.
Let h be the distance from home plate to second base.
According to the Pythagorean theorem, we have:
h^2 = 60^2 + 60^2
Simplifying this equation, we get:
h^2 = 3600 + 3600
h^2 = 7200
Taking the square root of both sides, we find:
h = √7200
To round to the nearest tenth, we get:
h ≈ 84.9 feet
So, the distance from home plate to second base is approximately 84.9 feet.