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NDA 1 2025 Maths, question 36

Topic: Trigonometry

Passage · Q36 to Q38

The sides of a triangle ABCABC are AB=3AB = 3 cm, BC=5BC = 5 cm and CA=7CA = 7 cm.

Q36

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?

  1. (a) I only
  2. (b) II only
  3. (c) Both I and IICorrect answer
  4. (d) Neither I nor II

Solution.

Answer: (c) Both I and II

  1. The longest side is 7 cm and 72=49>32+52=347^{2} = 49 > 3^{2} + 5^{2} = 34.
  2. The angle opposite it, ∠B\angle B, is therefore obtuse, proving I.
  3. The other two angles sum to 180∘−B<90∘180^{\circ} - B < 90^{\circ}.
  4. Their sum is acute, proving II.