In a triangle A B C , if A = 2 B and the sides opposite to the angles A , B , C are α + 1 , α - 1 and α respectively, then α =

Question

In a triangle A B C , if A = 2 B and the sides opposite to the angles A , B , C are α + 1 , α - 1 and α respectively, then α =, 3, 4, 5, 6

MARKS App · Accepted Answer

From sine rule: α + 1 sin A = α - 1 sin B = α sin C α + 1 sin 2 B = α - 1 sin B [From given data] ⇒ α + 1 2 sin B cos B = α - 1 sin B ⇒ cos B = α + 1 2 ( α - 1 ) . . . 1 From cosine rule: cos B = a 2 + c 2 - b 2 2 a c = ( α + 1 ) 2 + α 2 - ( α - 1 ) 2 2 ( α + 1 ) ( α ) = α 2 + 4 α 2 α ( α + 1 ) = α + 4 2 ( α + 1 ) . . . 2 From equations ( 1 ) & 2 , α + 1 2 ( α - 1 ) = α + 4 2 ( α + 1 ) ⇒ α 2 + 2 α + 1 = α 2 + 3 α - 4 ⇒ α = 5

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