Applications of the Pythagorean Theorem

Question

On a baseball field, it is 90 feet between bases. Determine the distance from home plate to second base. Then determine if this is the same as the distance from third base to first base.

 

home plate to second base:

 

first base to third base:

 

I have to show work.

 

Please explain.

Answer 1

A baseball diamond is actually a square, each leg of which is 90'.

 

The distance from home plate to second base can be determined by the Pythagorean theorem, a² + b² = c² where c is the hypotenuse, the distance from home plate to second base.

 

That distance is the square root of 90'² + 90'² = 8100 + 8100 = 16200, the square root of 16200 is 127.3'

 

Since the baseball diamond is a square, the distance from third base to first base is exactly the same, namely 127.3'