Question

With usual notations, if the angles A, B, C of a Δ ABC are in AP and b : c = `sqrt3 : sqrt2`.

Options

• 75°

• 55°

• 35°

• 45°

Answer 1

75°

Explanation:

In Δ ABC

∠A, ∠B, ∠C are in A.P

∴ 2∠B = ∠A + ∠C    ...(i)

and ∠A + ∠B + ∠C = 180°    ...(ii)

From Eqs. (i) and (ii), B = 60°

∴ `"b"/(sin "B") = "c"/(sin "C")`

`=> (sin "B")/(sin "C") = "b"/"c"`

`=> (sin 60^circ)/(sin "C") = sqrt3/sqrt2   ....[because "b" : "c" = sqrt3 : sqrt2]`

⇒ sin C = `(sqrt2 xx sqrt3)/(sqrt3 xx 2) = 1/sqrt2`

∴ sin C = sin 45°

⇒ C = 45°

∠A = 2∠B - ∠C = 120° - 45° = 75°