Question

In \( \Delta ABC \), if \( c^2 + a^2 - b^2 = ac \), then \( \angle B = \)

• A. \( \frac{\pi}{4} \)
• B. \( \frac{\pi}{3} \)
• C. \( \frac{\pi}{2} \)
• D. \( \frac{\pi}{6} \)

Hint:

In any triangle, applying the Law of Cosines helps relate the sides and angles of the triangle.

Answer 1

The Correct Option is C

Step 1: Use the Law of Cosines. 
The equation \( c^2 + a^2 - b^2 = ac \) is similar to the Law of Cosines, which states: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(\angle B) \] By substituting and simplifying, we find that \( \angle B = \frac{\pi}{2} \).

 tep 2: Conclusion. 
The correct answer is \( \frac{\pi}{2} \), so the correct option is (C).