In a triangle ABC, sinA : sinB : sinC = 1 : 2 : 3. If b = 4 cm, then the perimeter of the triangle is (1) 6 cm (2) 24 cm (3) 12 cm (4) 8cm

Answer: (3)

Given parameters:

sinA = 1

sinB = 2

sinC = 3

b = 4 cm

According to the sin rule

(a/sin A) = (b/sin B) = (c/sin C)

⇒ a = 4 × (sinA/sinB)

⇒ a = 4 × (1/2)

⇒ a = 2 cm

⇒ c = 4 × (sinC/sinB)

⇒ c = 4 × (3/2)

⇒ c = 6 cm

Adding three parameters we get

a + b + c = 2 + 4 + 6 = 12 cm

The perimeter of the triangle is = 12 cm.

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