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

Engineering

Mathematics

Basic Rules of Properties of Triangle

Question

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

$\frac{4}{\sqrt{3}}$

$4 \sqrt{3}$

$\frac{2}{\sqrt{3}}$

$2 \sqrt{3}$

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$∠ B = \frac{π}{3}, by sine Rule$

$sinA = \frac{1}{2}$

$\Rightarrow A = 30 °, a = 2, b = 2 \sqrt{3}, c = 4$

$Δ = \frac{1}{2} \times 2 \sqrt{3} \times 2 = 2 \sqrt{3} sq . cm$