In a triangle ABC, a = 4, b = 3, c = 2. What is cos 3C equal to ?

Let a, b, c be the lengths of sides BC, CA, AB respectively of a triangle ABC. If p is the perimeter and q is the area of the triangle, then what is $p(p-2a) \tan \left(\frac{A}{2}\right)$ equal to ?

Direction: Consider the following for the next two (02) items that follow.

The two vertices of and equilateral triangle are (0, 0) and (2, 2).

Consider the following statements:

1. The third vertex has at least one irrational coordinate.

2. The area is irrational.

Which of the above statements is/are correct?

The sides of a triangle are m, n and $\rm \sqrt{m^2+n^2+mn}$. What is the sum of the acute angles of the triangle?