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?
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. I only
- B. II and III only
- C. I and III only ✓
- D. I, II and III
Correct Answer: C. I and III only
Explanation
The angles are B=30^{\circ}, A=3(30^{\circ})=90^{\circ}, leaving C=60^{\circ}. The triangle is right-angled (I is true). The sides are in the ratio 2:1:\sqrt{3}, so no side is 3 times another (II is false). The angles 90^{\circ}, 60^{\circ}, 30^{\circ} form an AP (III is true).