Question

With usual notations, in triangle ABC, \( a = \sqrt{3} + 1 \), \( b = \sqrt{3} - 1 \) and \( \angle C = 60^\circ \), then \( A - B = \)

• A. 45°
• B. 60°
• C. 30°
• D. 90°

Hint:

For problems involving angles in triangles, the cosine rule is a very useful tool to calculate angles based on known sides.

Answer 1

The Correct Option is D

Step 1: Use the cosine rule.
Using the cosine rule in triangle ABC: \[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \] Given \( \angle C = 60^\circ \), we know that \( \cos 60^\circ = \frac{1}{2} \). Substituting the values of \( a \), \( b \), and \( C \), we can solve for the value of \( A - B \).
Step 2: Simplification.
After simplifying, we find that \( A - B = 90^\circ \). Therefore, the correct answer is \( 90^\circ \).
Step 3: Conclusion.
The correct answer is (D) 90°.