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NDA 1 2025 Maths, question 46

Topic: Trigonometry

Passage · Q46 to Q47

In a triangle ABCABC, two sides BCBC and CACA are in the ratio 2:12:1 and their opposite corresponding angles are in the ratio 3:13:1.

Q46

One of the angles of the triangle is

  1. (a) 15∘15^{\circ}
  2. (b) 30∘30^{\circ}Correct answer
  3. (c) 45∘45^{\circ}
  4. (d) 75∘75^{\circ}

Solution.

Answer: (b) 30∘30^{\circ}

  1. Write A=3θA = 3\theta and B=θB = \theta.
  2. By the sine rule, sin⁡3θ/sin⁡θ=2\sin 3\theta/\sin\theta = 2.
  3. Using sin⁡3θ=3sin⁡θ−4sin⁡3θ\sin 3\theta = 3\sin\theta - 4\sin^{3}\theta gives sin⁡2θ=1/4\sin^{2}\theta = 1/4.
  4. Since A+B=4θ<180∘A + B = 4\theta < 180^{\circ}, we have 0<θ<45∘0 < \theta < 45^{\circ}, so θ=30∘\theta = 30^{\circ}.
  5. The angles are 90∘,30∘,60∘90^{\circ},30^{\circ},60^{\circ}.