If in a triangle ABC, ∠ A = 30º and the area of triangle is 
, then prove that either
B = 4 C or C = 4 B.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
∠ A = 30° and Δ = 
bc sinA = 
a 2 ⇒ 
bc sin30° = 
a 2 ⇒ bc = 
a 2
⇒ sinB sinC = 
sin 2 A ⇒ sinB sinC = 
as sinA = 
⇒ cos(B – C) – cos (B + C) = 
⇒ cos (B – C) + cosA = 
⇒ cos(B – C) = 0 (as ∠ A = 30º ⇒ cos A = 
)
⇒ B – C = 90° or B – C = – 90°
But B + C = 150° as A = 30 A
case (i) : if B – C = 90°
and B + C = 150° ⇒ B = 120° and C = 30° ⇒ B = 4C
case (ii) : if B – C = – 90°
and B + C = 150° ⇒ B = 30° and C = 120° ∴ C = 4B.
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