Question

If angles of a triangle are in the ratio 1:2:3, find out the greatest angle​

Answer 1

Answer:

Let angles be x, 2x, 3x

So, by angle sum property of triangle

x+2x+3x=180°

6x=180°

x=30°

Largest angle 3x = 3×30°= 90°

Answer 2

$\huge \bold \color{green}༆ \mathfrak \red{required \: answer}༆$

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ratio of angles of a traingle us 1:2:3

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90°

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since ratio of angles is 1:2:3,

let angles of a triangle are 1x , 2x and 3x

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sum of angles of a triangle is 180°

$\implies \: 1x + 2x + 3x = 180 \\ \implies \: 6x = 180 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \implies \: x = 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now substitute the value of x in angles..

angles of triangle are;

$1 \times 30 = 30 \degree \\ \\ 2 \times 30 = 60 \degree \\ \\ 3 \times 30 = 90 \degree$

here 30° < 60° < 90°

so angle of 90° is greatest angle of triangle..

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• perimeter of ∆ = sum of sides of ∆
• area of ∆ = 1/2 × base × hight

by heron's formula..area of ∆ ;

$= \sqrt{s( s - a)(s - b)(s - c)} \\ \\ where \: s = \frac{a + b + c}{2}$

• hypotenuse is the greatest side of a right angle triangle
• sum of angles of a triangle is 180°
• angles opposite to equal sides are equal in a ∆
• sides opposite to equal angles are equal in a ∆
• exterior angle of a ∆ is equal to sum of two opposite sides of a ∆