Chapter 8.3, Problem 51AYU

To determine

To find: The distance between the fence in the dead centre to the third base.

Answer to Problem 51AYU

The distance between the fence in the dead centre to the third base is $245.45\text{ft}$ .

Explanation of Solution

Given information:

The distance from the home plate to the fence in dead centre in Wrigley Field is $400\text{ft}$ .

The given figure is,

  

Concept used:

Law of Cosines:

If ABC is a triangle with sides $a$ , $b$ , and $c$ , then

  $\begin{array}{l}\cos A=\frac{b^2+c^2-a^2}{2bc}\\ \cos B=\frac{a^2+c^2-b^2}{2ac}\\ \cos C=\frac{a^2+b^2-c^2}{2ab}\end{array}$

The distance between the fence in the dead centre to the third base is calculated as,

  $\begin{array}{l}\cos A=\frac{b^2+c^2-a^2}{2bc}\\ \cos 45°=\frac{{\left(400-90\right)}^2+{90}^2-a^2}{2\left(400-90\right)\left(90\right)}\\ a\approx 245.45\text{ft}\end{array}$

Hence, the distance between the fence in the dead centre to the third base is $245.45\text{ft}$ .