2
(√5,3)
The process is as follows
First, the sum of the two sides is greater than the third side.
The difference between the two sides is smaller than the third side.
The approximate value range of c is (1, 3).
Application of Cosine Theorem
Because the obtuse triangle ABC
Therefore, the angle C subtended by C must be greater than 90.
So cosc is negative.
Cosine theorem C = 5-4 COSC
cosc=(-c^2
+5)/4
So (5-c 2) < 0
The solution is c 2 > 5.
-√5