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
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6
Answer: (3) 12 cm
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.
Answered by
4
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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