More Baseball...Law of Cosines

[greatwhiteshark]

A Major League baseball diamond is actually a square 90 feet on a side. The pitching rubber is 60.5 feet from home plate on a line joining home plate and second base.

a) How far is it from the pitching rubber to first base?

b) How far is it from the pitching rubber to second base?

c) If a pitcher faces home plate, through what angle does he need to turn to face first base?

 

[soroban]

Hello, greatwhiteshark!

I'll get you started on this one . . .

A Major League baseball diamond is actually a square 90 feet on a side.
The pitching rubber is 60.5 feet from home plate on a line joining home plate and second base.

a) How far is it from the pitching rubber to first base?

         *F
   P*   /                The Pitcher, First Base, and
    |  /                  Home Plate form a triangle.
60.5| /90
    |/                  You know that PH = 60.5, FH = 90
    *                     and angle PHF = 45 degrees.
   H

You know two sides and the included angle.
You can use the Law of Cosines to find the third (opposite) side, PF.
. . . Go for it!

 

[greatwhiteshark]

Yes but...

Where did 45 degrees come from?