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

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NDA (Held On: 21 Apr 2019) Maths Previous Year paper
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  1. 1 : 2 : 3
  2. 3 : 2 : 1
  3. 1 : √3 : 2
  4. 1 : √3 : √2

Answer (Detailed Solution Below)

Option 3 : 1 : √3 : 2
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Detailed Solution

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Concept:

Sine rule:

Calculation:

Given: The angles of a triangle ABC are in the ratio 1 : 2 : 3

Let, ∠ A = x, ∠ B = 2x and ∠ C = 3x

⇒ ∠ A + ∠ B + ∠ C = 180°     ...(By angle sum property)

⇒ x = 30°

⇒ ∠ A = 30°, ∠ B = 60° and ∠ C = 90°

As we know that, 

⇒ a = k/2, b = √3 k/2 and c = k

Hence, a : b : c = 1 : √3 : 2

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