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NDA 2023 Maths · Mathematics · Properties of Triangles · medium

In a triangle ABC, the angles satisfy A:B:C=1:2:3. The ratio of the sides a:b:c is

Single correct option

In a triangle ABCABC, the angles satisfy A:B:C=1:2:3A:B:C=1:2:3. The ratio of the sides a:b:ca:b:c is
  1. A. 1:2:31:2:3
  2. B. 1:2:31:\sqrt2:\sqrt3
  3. C. 2:3:12:\sqrt3:1
  4. D. 1:3:21:\sqrt3:2
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Answer: (D) 1:3:21:\sqrt3:2

The angles are 30∘,60∘,90∘30^\circ,60^\circ,90^\circ because 1+2+3=61+2+3=6 parts make 180∘180^\circ. By the sine rule a:b:c=sin⁡30∘:sin⁡60∘:sin⁡90∘=12:32:1=1:3:2a:b:c=\sin30^\circ:\sin60^\circ:\sin90^\circ=\tfrac12:\tfrac{\sqrt3}2:1=1:\sqrt3:2. Option 1:2:31:2:3 wrongly assumes sides are proportional to angles.
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Original question written in the NDA 2023 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