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. Consider the following statements: I. The triangle is right-angled. II. One of the sides of the triangle is 3 times the other. III. The angles A, C and B of the triangle are in AP. Which of the statements given above is/are correct?
A.I only
B.II and III only
C.I and III only✓ Correct
D.I, II and III
Explanation
With B = 30°, A = 90°, so C = 60°. So the triangle is right-angled (I correct). Sides: BC = 2k, CA = k, AB = k√3 — none is 3 times another, so II is wrong. Angles A=90°, C=60°, B=30° form AP with common difference -30°, so III is correct.
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