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NDA 2016 Maths · Mathematics · Properties of Triangles · easy

In a triangle ABC, A=45^°, B=60^° and a=√6. The length of side b is

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In a triangle ABCABC, A=45∘A=45^\circ, B=60∘B=60^\circ and a=6a=\sqrt6. The length of side bb is
  1. A. 33
  2. B. 232\sqrt3
  3. C. 323\sqrt2
  4. D. 6\sqrt6
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Answer: (A) 33

By the sine rule, b=asin⁡Bsin⁡A=6⋅3/22/2=6⋅32=9=3b=\dfrac{a\sin B}{\sin A}=\sqrt6\cdot\dfrac{\sqrt3/2}{\sqrt2/2}=\sqrt6\cdot\dfrac{\sqrt3}{\sqrt2}=\sqrt9=3. Swapping the angles gives 6⋅2/3=2\sqrt6\cdot\sqrt2/\sqrt3=2, which is not an option; 6\sqrt6 itself ignores the ratio of sines.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake