Chapter 12.6, Problem 5P

To determine

To determine the distance between Newtown from Littleton.

Answer to Problem 5P

The distance between Newtown and Littleton is 16.64mi

Explanation of Solution

Given information :

Given distances are 10 mi and 8 mi.

To find the distance between the two town we shall find the third side of the triangle.

  

Here we shall use the cosine rule.

Cosine formula states that,

  $\cos A=\frac{b^2+c^2-a^2}{2bc}$

Hence we get,

  $\begin{array}{l}\cos {135}^{\circ }=\frac{8^2+{10}^2-A{C}^2}{2\left(8\right)\left(10\right)}\\ -113.14=164-A{C}^2\\ A{C}^2=277\\ AC=16.64\end{array}$

Hence the distance between Newtown and Littleton is 16.64mi