Question

A baseball diamond is a square with the sides measuring at 90 feet. The distance from center field fence to home plate is 400 feet, how far is third base to the center field fence?

Answer 1

We can treat it like a triangle. The line from home plate bisects the 1st base

and 3rd base angle; so it's 45 degrees; call it angle B. The side opposite, b is

the side we want to find, (from 1st to dead center)

:

Let angle A be at 1st base then side a = 401

Let angle C is at center field, then side c = 90

:

Use the law of cosines:

b^2 = a^2 + c^2 - 2(a*c)Cos(B)

:

b^2 = 401^2 + 90^2 - 2(401*90)Cos(45)

:

b^2 = 16080 + 8100 - 2(36090)*.7071

:

b^2 = 168901 - 51038.5

:

b = √117863

b = 343.3 ft from 1st to straight-a-away center