Erica plotted the three towns closest to her house on a graph with town aa at (9, 12), town bb at (9, 7) and town cc at (1, 1). she drew the triangle joining the 3 points. which lists the angles formed in size, smallest to largest?

To compute the distance between the points, we can apply the distance formula as shown below.



In which x₁ and x₂ are the x-coordinates and y₁ and y₂ are the y-coordinates of the two points. Thus, applying this with the segments AABB, AACC, and BBCC, we have





Now that we have the lengths of all the sides of ΔAABBCC, we can find the missing angles using the Law of Cosines.

Generally, we have



or



Hence, we have





Simplifying this, we have



 

Thus, from this, we can arrange the angles from smallest to largest: ∠CC, ∠AA, and ∠BB.

 ∠CC, ∠AA, and ∠BB