# Open Middle Problem: Law of Cosines (V2)

- Author:
- Tim Brzezinski

- Topic:
- Cosine, Geometry, Trigonometry

Creation of this problem was inspired by this OpenMiddle problem posted by Erik Lee.
It's not the same problem, but rather a spin-off.
In the triangle below, you can move the

**LARGE POINTS**to adjust its side lengths.- The
**LARGE POINTS**on the left control the length of the left side. - The
**LARGE POINTS**on the right control the length of the right side. - The
**LARGE POINTS**on the bottom control the length of the bottom side.

## Given the condition that the integers 1-9 must appear at most 1 time each, what is the largest possible interior angle you can create? What is the smallest?

What is the measure of the largest angle you can possibly make under this "no repeated values" constraint?

What is the measure of the smallest angle you can possibly make under this "no repeated values" constraint?