Question

The meaguores Of a triange che in the
ratio 11:12:13 Find the measures of
angles of that triangle:​

Answer 1

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$\green{\underline \bold{Given :}}$

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• Ratio of angles of triangle 11:12:13

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$\red{\underline \bold{To \: Find:}}$

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• The measure of each angle

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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• Let the angles be a , b , c

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Also,

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• The angles are 11x , 12x , 13x

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$\underline{\bold{\texttt{We know that :}}}$

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$\purple\longrightarrow$ $\bf a + b + c = 180°$

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$\sf \dashrightarrow 11x + 12x + 13x = 180°$

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$\sf \longmapsto 36x = 180°$

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$\sf \longmapsto x = \dfrac { 180 } { 36 }$

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$\bf \dashrightarrow x = 5$

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So angles will be ,

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• 11x = 11 × 5 = 55°

• 12x = 12 × 5 = 60°

• 12x = 13 × 5 = 65°

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Additional information about triangle

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⇴ Types of triangle

• Scalene Triangle: All the sides and angles are unequal.

• Isosceles Triangle: It has two equal sides. Also, the angles opposite these equal sides are equal.

• Equilateral Triangle: All the sides are equal and all the three angles equal to 60°.

• Acute Angled Triangle: A triangle having all its angles less than 90°.

• Right Angled Triangle: A triangle having one of the three angles exactly 90°.

• Obtuse Angled Triangle: A triangle having one of the three angles more than 90°.

⇴ Properties related to triangle

• Area of triangle = 1/2 × base × height

• Area of triangle by heron's formula = √[s(s – a)(s – b)(s – c)] Where "s" is semi perimeter and "a" , "b" , "c" are sides.

• Perimeter of triangle = side1 + side2 + side3

• The exterior angle of a triangle is always equal to the sum of the interior opposite angles.