Chapter 4.8, Problem 4CYP

To determine

To Prove:

Coordinate proof to that the west Texas triangle is approximately isosceles.

Explanation of Solution

Give information:

  

Proof:

Points of midland Odessa is $\left(102.3,31.9\right)$ , san Angelo $\left(100.5,31.4\right)$ , Albany Abilene $\left(99.3,32.7\right)$

  $OS$ is calculated as,

  $\begin{array}{l}OS=\sqrt{{\left(102.3-100.5\right)}^2+{\left(31.9-31.4\right)}^2}\\ =\sqrt{3.24+0.25}\\ =\sqrt{3.49}\\ \simeq 1.87\end{array}$

  $SA$ is calculated as,

  $\begin{array}{l}SA=\sqrt{{\left(100.5-99.3\right)}^2+{\left(31.4-32.7\right)}^2}\\ =\sqrt{1.44+1.69}\\ =\sqrt{3.13}\\ \simeq 1.77\end{array}$