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AP EAMCET20224 Jul 2022Morning ShiftMathematicsProperties of TrianglesActual

If the angles of a triangle A B C are in the ratio 1 : 2 : 3 , then the corresponding sides are in the ratio

Options

  1. A1 :   2 :   3
  2. B3 :   2 :   1
  3. C1 : 3 : 2
  4. D1 : 3 : 2

Correct answer

C. 1 : 3 : 2

Step-by-step solution

Given that angles of a triangle are in the ratio 1 : 2 : 3 ∵   From angle sum property, we have, sum of all angles of a triangle = 180 ° And angle ratio is 1 : 2 : 3 Hence, angles are 30 ° ,   60 ° ,   90 ° respectively. So, according to sine rule a sin A = b sin B = c sin C ⇒ a sin 30 ° = b sin 60 ° = c sin 90 ° ⇒ a 1 2 = b 3 2 = c 1 ⇒ a 1 = b 3 = c 2 Hence, ratio of a : b : c will be 1 : 3 : 2

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