finding distance

Question

given that a baseball field has 90' between bases and 60.5' from home plate to the top of the pitcher's mound, and determine how far it is from the top of the pitcher's mound to second base.

Answer 1

Hi Waristat,

 

Let's begin by drawing a diagram of what is given in the problem.

 

Click this link (https://dl.dropbox.com/s/26jylry1sh908wo/Baseball_Diamond.png?raw=1) to view our diagram pertaining to the solution below.

 

As we can see, the pitcher's mound (point P) lies on the diagonal of square (HFST) connecting home plate (point H) with second base

(point S).  

 

Since a square has all equal sides and all vertex angles are equal right angles, we can use the Pythagorean theorem to find our unknown distance (x) from the pitcher's mound (point P) to second base

(point S):

    (90)² + (90)² = (x + 60.5)²

    8100 + 8100 = (x + 60.5)²

    (x + 60.5)² = 16200

    x + 60.5 = √16200

    x = √16200 - 60.5

    x = 127.3 - 60.5

    x = 66.8’

 

A good diagram is often helpful in seeing what relationship is best used to solve a problem.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.