Question

the angles of a traingle are in the ratio 5:4:1 find the angles​

Answer 1

Given -

• Angles of a triangle are in the ratio 5:4:1.

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To find -

• Measures of each angle.

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Solution -

Firstly,

• Let the ratio of angles be x.

Then,

• First angle = 5x
• Second angle = 4x
• Third angle = x

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As we know that sum of all angles of a triangle is 180°. [Angle sum property of a triangle]

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$\tt\dashrightarrow{5x + 4x + x = 180}$

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$\tt\dashrightarrow{10x = 180}$

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$\tt\dashrightarrow{x = \dfrac{180}{10}}$

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$\tt\dashrightarrow{x = 18}$

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We get,

• Value of x = 18.

By putting the value of x, we can find all the required angles.

⇢ First angle = 5x = 90°

⇢ Second angle = 4x = 72°

⇢ Third angle = x = 18°

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$\underline{\sf{Hence,\: required\: angles\: are\: 90^{\circ},\: 72^{\circ}\: and\: 18^{\circ}.}}$

Answer 2

GivEn:

• Ratio of angles of a triangle = 5:4:1

To find:

• Sides of triangle?

Solution:

☯ Let side in common be x cm.

We know that,

★ Sum of its all sides = 180°

Here,

Sides of triangle = 5x,4x and 1x

Therefore,

⇒ 5x + 4x + x = 180°

⇒ 10x = 180°

⇒ x = 180/10

⇒ x = 18

∴ Thus, The value of x is 18.

Hence,

• Angles of the triangle are 90°,72° and 18°

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More to know:

• Area of triangle = ½ × base × height

• Heron's Formula = √s(s - a)(s - b)(s - c)

• Sum of all angles of a triangle is 180°.

★ Trigonometric Identities :

• sin²θ + cos²θ = 1
• sec²θ - tan²θ = 1
• csc²θ - cot²θ = 1

★ Trigonometric relations :

• sinθ = 1/cscθ
• cosθ = 1 /secθ
• tanθ = 1/cotθ
• tanθ = sinθ/cosθ
• cotθ = cosθ/sinθ

★ Trigonometric ratios :

• sinθ = opp/hyp
• cosθ = adj/hyp
• tanθ = opp/adj
• cotθ = adj/opp
• cscθ = hyp/opp
• secθ = hyp/adj