Question

If \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm and \( BC = 6 \) cm in triangle \( ABC \), then the value of \( \angle B \) will be:

• A. 90°
• B. 60°
• C. 120°
• D. 45°

Hint:

Use the cosine rule to find an angle in a triangle when you know the lengths of all three sides.

Answer 1

The Correct Option is B

We are given a triangle \( ABC \) with sides \( AB = 6\sqrt{3} \), \( AC = 12 \), and \( BC = 6 \). We need to find \( \angle B \).
Step 1: Apply the cosine rule.
The cosine rule states that: \[ \cos B = \frac{AC^2 + BC^2 - AB^2}{2 \times AC \times BC} \] Substitute the given values: \[ \cos B = \frac{12^2 + 6^2 - (6\sqrt{3})^2}{2 \times 12 \times 6} \] \[ \cos B = \frac{144 + 36 - 108}{144} \] \[ \cos B = \frac{72}{144} = \frac{1}{2} \]
Step 2: Calculate \( \angle B \).
Since \( \cos B = \frac{1}{2} \), we know that: \[ \angle B = 60^\circ \]
Step 3: Conclusion.
Therefore, the value of \( \angle B \) is 60°. The correct answer is (B).