Chapter MPS, Problem 14.4MPS

a.

To determine

Find the distance between Mark and Francine.

Answer to Problem 14.4MPS

  $8unit$

Explanation of Solution

Given information:

Francine lives at $O$ . Norman lives at $N$ . Mark lives at $M$ . School is at $J$ . $\angle ais38°$ and $\angle bis42°$ . Francine lives $1$ mile from school. Round to the nearest hundredth, if necessary.

  

Calculation:

Consider the graph:

  

The point $O$ is at $(0,0)$ and the point $M$ is at $(8,0)$ .

So, the distance is calculated below.

  $\begin{array}{l}8-0\\ =8\end{array}$

Hence, the distance is $8unit$ .

b.

To determine

Find the closest distance.

Answer to Problem 14.4MPS

  $0.19unit$

Explanation of Solution

Given information:

Francine lives at $O$ . Norman lives at $N$ . Mark lives at $M$ . School is at $J$ . $\angle ais38°$ and $\angle bis42°$ . Francine lives $1$ mile from school. Round to the nearest hundredth, if necessary.

  

Calculation:

Consider thye graph:

  

The point $O$ is at $(0,0)$ and the point $N$ is at $(2,0)$ .

The point $J$ is at $(2,10)$ .

The distance between School and Norman is calculated below.

  $\begin{array}{l}(10-0)\\ =10\end{array}$

The distance between School and Norman is calculated below.

  $\begin{array}{l}\sqrt{{\left(2-0\right)}^2+{\left(10-0\right)}^2}\\ =\sqrt{4+100}\\ =\sqrt{104}\\ =10.19\end{array}$

The closest distance is calculated below.

  $\begin{array}{l}10.19-10\\ =0.19\end{array}$

Hence, the closest distance is $0.19unit$ .