Consider the following statements : I. The triangle is obtuse-angled triangle. II. The sum of acute angles of the triangle is also acute. Which of the statements given above is/are correct?
Consider the following for the three (03) items that follow : The sides of a triangle ABC are AB=3\text{ cm}, BC=5\text{ cm} and CA=7\text{ cm}.
- A. I only
- B. II only
- C. Both I and II ✓
- D. Neither I nor II
Correct Answer: C. Both I and II
Explanation
Let a=5, b=7, c=3. By Cosine Rule, the largest angle B is \cos B = \frac{a^2+c^2-b^2}{2ac} = \frac{25+9-49}{30} = -1/2. Thus \angle B = 120^{\circ}, making it an obtuse triangle (Statement I is true). The sum of the remaining angles is 180^{\circ} - 120^{\circ} = 60^{\circ}, which is acute (Statement II is true).