Chapter 8.3, Problem 51AYU

To determine

How far is it from the fence in dead centre to third base?

Answer to Problem 51AYU

  $\boxed{\text{342}.\text{3ft}}$

Explanation of Solution

Given information:

The distance from home plate to the fence in dead centre in Wrigley Field is 400 feet. How far is it from the fence in dead centre to third base?

Calculation:

From the figure we can say that the distance from the fence to the home plate and the third base forms a triangle with two side lenghts 400 ft and 90 ft and an included angle of $45°$ .

Use the Law of Cosines to find the distance from the fence to the third base.

Let the required distance be $x$ .

  $x^2={400}^2+{90}^2-\mathrm{2.400.90.}\cos 45°$

  $=160000+8100-50911.6$

  $=117188.4$

Take square root on both the sides.

  $\sqrt{x^2}=\sqrt{117188.4}$

  $x\approx 342.3$

Hence, the fence in dead centre is about $\boxed{\text{342}.\text{3ft}}$ from the third base.