Math Quesstion!?

Question

Ok, heres the link to the diamond http://www.geom.uiuc.edu/~demo5337/Group3/bball.html

NOW, how do you figure out what the first and third bases are. Please I need EXPLANATIONS

Answer 1

Pythagorean theorem says the sum of the squares of the sides equals the square of the hypotenuse
You have the triangle from home to first and first to second and home to first
You have sides at 90 feet and the hypotenuse x
90^2+90^2=x^2
or 2(90^2)=x^2
sqrt of each side
sqrt 2 times 90=x
1.414*90= 127.26 feet from home to second or from third to first.

Answer 2

How to figure out which base is 1st?

One base (home plate) is shaped differently from the others. It has 5 sides. The others are square cushions.

The batter stands at home plate. When he becomes a runner, he must go counterclockwise around the bases. i.e., he starts to his right when he faces the inside of the diamond (or, if you prefer the mathematical approach, the inside of the diamond is to his left as he moves around).

The bases are numbered according to the order in which the runner reaches them.

Answer 3

The hypotenuse length is x.
x is the distance between home plate and second base.
Because it is square, it is also the distance from 1st to 3rd base.
x^2 = 90^2 + 90^2
x^2 = 8100 + 8100
x^2 = 16200
x = sqrt(16200)
x = 90sqrt(2) = 127.28

Answer 4

x^2 = 90^2 + 90^2

x = squrt (90^2 + 90^2)

the distance from the homeplate to the 2nd base is the same distance from the 1st base to the 3rd base.

Answer 5

use the pythagorean theorem. cut the square in half to form two right triangles. 90 is the length of the two legs.

a^2 + b^2 = c^2

(90)^2 + (90)^2 = c^2

c = 90*sqrt(2)