The bases in a softball diamond are located at the corners of a square with an area A of 3600 square feet.
We want to calculate the distance between second base and home plate. To do so we need to find the length of each side. Since the area is 3600 square feet, we can find the length s using the formula for the area of a square.
A = s^2Let's substitute A= 3600 into the formula and solve it for s.
The length of each side of the square is 60 feet. We will divide the given square into four right triangles. Note that the segment between each base divides the right angle into two angles of 45^(∘).
Next, we will choose one triangle to look at.
We have the value of angle θ and the length of hypotenuse h. Therefore, we can use the cosine function to calculate the value of x.
cos θ = Adjacent/Hypotenuse= x/h
Let's substitute θ= 45^(∘) and h= 60 into the formula and solve it for x.
Finally, we will multiply this value by two to find the distance between the second base and home plate.
d = 2x ⇒ d=84.8
The distance is about 84.8 feet.
