Question

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Answer 1

Explanation:

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If the angles of a triangle are in the ratio 1:2:3, then what ratio is the side in respect of the triangle?

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Let the angles of a triangle are x° ,2x°. 3x°.acordingly:-

x°+2x° +3x°=180°

6x°=180°

or. x=30°

Angles are 30° , 60°. and. 90°.

Let a. , b and c units be the length of the sides of the triangle. Applying

sine rule

a/sin30° = b /sin60° = c/sin90°

2.a/1= 2b/√3. = c/1

a= c/2 , b= (c.√3)/2.

a : b : c = c/2. : c√3/2. : c. = 1/2. : √3/2 : 1. or 1 : √3. : 2. Answer.

Answer 2

Explanation:

$Let A=θ,B=2θ,C=3θ</p><p> \\ ∵A+B+C=π</p><p> \\ ⇒θ+2θ+3θ=π</p><p> \\ ⇒6θ=π</p><p> \\ ⇒θ=6π</p><p> \\ ∴A=θ=6π</p><p> \\ B=2θ=2×6π=3π</p><p> \\ C=3θ=3×6π=2π</p><p> \\ ∴a:b:c \: = \: sin6π:sin3π:sin2π</p><p> \\ ⇒a:b:c=21:23:1</p><p> \\ or \: a:b:c=1:3:2</p><p></p><p>$

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