Chapter 12.5, Problem 20MCQ

To determine

To find: How far would Eric need to walk.

Answer to Problem 20MCQ

Distance eric needs to walk to each camp $=d=6.15$ miles

Explanation of Solution

Given information:

Let E be the point of final position of Eric.

Z be point of the camp.

Another point which is ${120}^0$ be D.

  $\begin{array}{l}e=4.5\\ z=2.5\\ D={120}^0\end{array}$

Given

  $\begin{array}{l}e=4.5\\ z=2.5\\ D={120}^0\end{array}$

Use law of cosines

We get

  $\cos \left(D\right)=\frac{e^2+z^2-d^2}{2ez}$

On substituting values

We get

  $\begin{array}{l}\cos \left(D\right)=\frac{e^2+z^2-d^2}{2ez}\\ \Rightarrow \cos \left({120}^0\right)=\frac{{\left(4.5\right)}^2+{\left(2.5\right)}^2-d^2}{2\left(4.5\right)\left(2.5\right)}\\ \Rightarrow -0.5=\frac{20.25+6.25-d^2}{22.5}\\ \Rightarrow -11.25=26.5-d^2\\ \Rightarrow d^2=26.5+11.25\\ \Rightarrow d^2=37.75\\ \Rightarrow d=\sqrt{37.75}\\ \Rightarrow d=6.15\end{array}$

Therefore,

Distance eric needs to walk to each camp $=d=6.15$ miles