NDA 2025 · PYQ · Trigonometry / Triangles · medium
The sides of a triangle ABC are AB = 3 cm, BC = 5 cm and CA = 7 cm. 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?
A.I only
B.II only
C.Both I and II✓ Correct
D.Neither I nor II
Explanation
Largest side CA = 7 opposite angle B. cosB = (AB² + BC² - CA²)/(2·AB·BC) = (9 + 25 - 49)/30 = -15/30 = -1/2, so B = 120°, obtuse. Statement I correct. Sum of acute angles A + C = 180° - 120° = 60°, which is acute. Statement II correct. Both correct.
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