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Properties of Triangle
Properties of Triangle
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Question

The angles A, B and C of a triangle ABC are in A.P. and a : b = 1 : 3\sqrt 3 . If c = 4 cm, then the area (in sq. cm) of this triangle is :

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Solution

From the question 2B = A + C & A + B + C = π\pi ⇒\Rightarrow 3B = π\pi ⇒\Rightarrow B = π3{\pi \over 3} ∴A+C=2π3σ\therefore A + C = {{2\pi } \over 3}\sigma ab=13{a \over b} = {1 \over {\sqrt 3 }} 2Rsin⁡A2Rsin⁡B=13{{2R\sin A} \over {2R\sin B}} = {1 \over {\sqrt 3 }} sin A = 12{1 \over 2} ∴\therefore A = 30 o ∴\therefore a = 2, b = 23\sqrt 3, c = 4 Δ=12×23×2=23\Delta = {1 \over 2} \times 2\sqrt 3 \times 2 = 2\sqrt 3

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