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Question
The angles of a triangle ABC, are in Arithmetic Progression and if b : c = `sqrt(3) : sqrt(2)`, find ∠A
Solution
Given that the angles A, B, C are in A. P.
∴ 2B = A + C
Also A + B + C = 180°
B + (A + C) = 180°
B + 2B = 180°
3B = 180°
⇒ B = 60°
A + C = 2B
= 2 × 60°
= 120°
`"b"/sin"B" = "c"/sin"C"`
`"b"/"c" = sin"B"/sin"C"` ......(1)
Given b : c = `sqrt(3) : sqrt(2)`
∴ (1) ⇒ `sqrt(3)/sqrt(2) = (sin 60^circ)/sin "C"`
`sqrt(3)/sqrt(2) = (sqrt(3)/2)/sin"C"`
`sqrt(3)/sqrt(2) = sqrt(3)/(2sin"C")`
sin C = `1/sqrt(2)`
⇒ C = 45°
A + 45° = 120°
A = 120° – 45° = 75°
A = 75°
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