In the triangle shown, n is a positive integer, and \(\angle A > \angle B > \angle C\). How many possible values of n are there?

Guest Mar 26, 2020

#1**+2 **

**Answer: \(\frac{8}{3} **

**Explanation:**

The largest angle's opposite side is the largest length of the triangle.

So \(2n+12>2n+7>3n-3\).

Take the last two inequalities and get \(n<10\)

Additionally, we can apply the triangle inequality and get \(2n+7+3n-3>2n+12\)

Solve to get \(3n>8\), and n>8/3.

So \(\frac{8}{3} .

You are very welcome!

:P

(I'm not completely sure about my answer, if someone could double check that would be great!)

CoolStuffYT Mar 26, 2020