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NDA 2 2024 Maths, question 23

Topic: Trigonometry

Q23

In a triangle ABCABC

acos⁡A=bcos⁡B=ccos⁡C\frac{a}{\cos A}=\frac{b}{\cos B}=\frac{c}{\cos C}

What is the area of the triangle if a=6 cma=6\text{ cm}?

  1. (a) 93 square cm9\sqrt{3}\text{ square cm}Correct answer
  2. (b) 12 square cm12\text{ square cm}
  3. (c) 183 square cm18\sqrt{3}\text{ square cm}
  4. (d) 24 square cm24\text{ square cm}

Solution.

Answer: (a) 93 square cm9\sqrt{3}\text{ square cm}

  1. By the sine rule a=2R sin A, so a/cos A=2R tan A, and similarly for B,C.
  2. The equal ratios force equal tangents and hence equal angles in a triangle.
  3. It is equilateral with side 6.
  4. Area=(√3/4)6²=9√3 cm².