The sides of a triangle are in the ratio 1:3:2 then the angles of the triangle are in the ratio

Let a:b:c=1:3:2⇒c2=a2+b2∴Δle is right angled at C(or)C=90° & ab=13.tanA=ab=13⇒A=30°&B=60°∴A:B:C=1:2:3

The sides of a triangle are in the ratio 1:3:2 then the angles of the triangle are in the ratio

Let a:b:c=1:3:2⇒c2=a2+b2∴Δle is right angled at C(or)C=90° & ab=13.tanA=ab=13⇒A=30°&B=60°∴A:B:C=1:2:3

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The sides of a triangle are in the ratio $1 : \sqrt{3} : 2$ then the angles of the triangle are in the ratio

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$1 : 3 : 5$

$2 : 3 : 2$

$3 : 2 : 1$

$1 : 2 : 3$

answer is D.

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Detailed Solution

Let $a : b : c = 1 : \sqrt{3} : 2 \Rightarrow c^{2} = a^{2} + b^{2}$
$∴ Δ l e$ is right angled at $C$
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$(o r) C = 90 ° & \frac{a}{b} = \frac{1}{\sqrt{3}} .$

$\tan A = \frac{a}{b} = \frac{1}{\sqrt{3}}$
$\Rightarrow A = 30 ° & B = 60 °$
$∴ A : B : C = 1 : 2 : 3$

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The sides of a triangle are in the ratio $1 : \sqrt{3} : 2$ then the angles of the triangle are in the ratio