A triangle with sides $a,b,c$ is called a good triangle if $a^2,b^2,c^2$ can form a triangle. How many of below triangles are good?

(i) $40^{\circ}, 60^{\circ}, 80^{\circ}$

(ii)  $10^{\circ}, 10^{\circ}, 160^{\circ}$

(iii) $110^{\circ}, 35^{\circ}, 35^{\circ}$

(iv) $50^{\circ}, 30^{\circ}, 100^{\circ}$

(v) $90^{\circ}, 40^{\circ}, 50^{\circ}$

(vi) $80^{\circ}, 20^{\circ}, 80^{\circ}$


$ 
\textbf{(A)}\ 1
\qquad\textbf{(B)}\ 2
\qquad\textbf{(C)}\ 3
\qquad\textbf{(D)}\ 4
\qquad\textbf{(E)}\ 5
$
To determine if a triangle with sides \(a, b, c\) is a good triangle, we need to check if \(a^2, b^2, c^2\) can form a triangle. This is equivalent to checking if the triangle is acute, as the squares of the sides of an acute triangle will also form a triangle.

We will analyze each given triangle to see if it is acute.

1. **Triangle with angles \(40^\circ, 60^\circ, 80^\circ\):**
   - All angles are less than \(90^\circ\), so this triangle is acute.
   - Therefore, this triangle is a good triangle.

2. **Triangle with angles \(10^\circ, 10^\circ, 160^\circ\):**
   - The angle \(160^\circ\) is greater than \(90^\circ\), so this triangle is obtuse.
   - Therefore, this triangle is not a good triangle.

3. **Triangle with angles \(110^\circ, 35^\circ, 35^\circ\):**
   - The angle \(110^\circ\) is greater than \(90^\circ\), so this triangle is obtuse.
   - Therefore, this triangle is not a good triangle.

4. **Triangle with angles \(50^\circ, 30^\circ, 100^\circ\):**
   - The angle \(100^\circ\) is greater than \(90^\circ\), so this triangle is obtuse.
   - Therefore, this triangle is not a good triangle.

5. **Triangle with angles \(90^\circ, 40^\circ, 50^\circ\):**
   - The angle \(90^\circ\) is exactly \(90^\circ\), so this triangle is right.
   - Therefore, this triangle is not a good triangle.

6. **Triangle with angles \(80^\circ, 20^\circ, 80^\circ\):**
   - All angles are less than \(90^\circ\), so this triangle is acute.
   - Therefore, this triangle is a good triangle.

From the analysis, the triangles that are good triangles are:
- (i) \(40^\circ, 60^\circ, 80^\circ\)
- (vi) \(80^\circ, 20^\circ, 80^\circ\)

Thus, there are 2 good triangles.

The final answer is \(\boxed{2}\)