One of the angles of the triangle is
Consider the following for the two (02) items that follow : In a triangle ABC, two sides BC and CA are in the ratio 2:1 and their opposite corresponding angles are in the ratio 3:1.
- A. 15^{\circ}
- B. 30^{\circ} ✓
- C. 45^{\circ}
- D. 75^{\circ}
Correct Answer: B. 30^{\circ}
Explanation
Let a = 2k and b = k. Also A = 3B. By the Sine Rule, \frac{\sin A}{\sin B} = \frac{a}{b} = 2. So \frac{\sin 3B}{\sin B} = 2. Using \sin 3B = 3\sin B - 4\sin^3 B, we get 3 - 4\sin^2 B = 2 \implies \sin^2 B = 1/4 \implies \sin B = 1/2. Thus B = 30^{\circ}.