SATHEE: Properties of Triangles 2 Question 4

Properties of Triangles 2 Question 4

4. The sides of a triangle are in the ratio $1 : \sqrt{3} : 2$ , then the angles of the triangle are in the ratio $(2004, 1 M)$

(a) $1 : 3 : 5$

(b) $2 : 3 : 2$

(d) $1 : 2 : 3$

Fill in the Blank

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Answer:

Correct Answer: 4. (d)

Solution:

Let $a : b : c = 1 : \sqrt{3} : 2 \Rightarrow c^{2} = a^{2} + b^{2}$

$∴$ Triangle is right angled at $C$ .

$∠ C = 90^{\circ}$

and

$\frac{a}{b} = \frac{1}{\sqrt{3}}$

In $△ B A C, \tan A = \frac{a}{b} = \frac{1}{\sqrt{3}}$

$\Rightarrow A = 30^{\circ}$

and $B = 60^{\circ}$

$[∵ A + B = 90^{\circ}]$

$∴$ Ratio of angles, $A : B : C = 30^{\circ} : 60^{\circ} : 90^{\circ} = 1 : 2 : 3$

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Properties of Triangles 2 Question 4

4. The sides of a triangle are in the ratio 1:3:2, then the angles of the triangle are in the ratio (2004,1M)

Fill in the Blank

Answer:

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4. The sides of a triangle are in the ratio $1 : \sqrt{3} : 2$ , then the angles of the triangle are in the ratio $(2004, 1 M)$