Question

A baseball diamond is a square that is 90' on each side. If a player throws the ball from 2nd base to home, how far will the ball travel?

Answer 1

So we are given that each side of a square is 90 feet.

By finding how far the ball will travel, we are basically finding the distance from 2nd base to home

Well, let's picture a baseball field, and we find out that they are diagonally across from one another.

Well, let's draw a diagonal connecting home to 2nd base.

Since the field is a square, it has a right angle at 1st base

We now know 2 legs in a right triangle, that calls for the Pythagorean Theorem

(You could also do 45-45-90 special right triangle, which would give you the answer very quickly)

So we have `90^2 + 90^2 = c^2`

Which is `16200 = c^2`

We are finding `c`, so `sqrt(16200) = c`

We can simplify this to `sqrt(162*100)` which is `10sqrt(162)`

Then we can simplify this to `10sqrt(81*2)`, which is `10*9sqrt(2)`

Finally, we multiply the values outside of the root to get our final answer `90sqrt2`

And we are done.