In δabc, a = 2, b = 3, and c = 4. find the value of cosc. is the triangle acute, right, or obtuse?

4^2 = 3^2 + 2^2 - 2  * 3 * 2 * cosC <=> 16 = 13 - 12 * cosC <=> 12 * cosC = -3 <=> cosC = - 1/4.

The applicable formula is known as the law of cosines
C² =  a² + b² -2abcosC
cosC  =       ( a² + b² - c²)/2ab
           =     ( 2² + 3² - 4²)/2*2*3
           =    (13-16)/12
           =    -3/12
           =    -1/4