Question

The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is​

Answer 1

Step-by-step explanation:

(a) Given, the ratio of angles of a triangle is 5 : 3 : 7.

Let angles of a triangle be ∠A,∠B and ∠C.

Then, ∠A = 5x, ∠B = 3x and ∠C = 7x

In ΔABC, ∠A + ∠B + ∠C = 180° [since, sum of all angles of a triangle is 180°]

5x + 3x + 7x = 180°

⇒ 15x = 180°

x = 180°/15= 12°

∠A = 5x = 5 x 12° = 60°

∠B = 3x= 3 x 12°= 36°

and ∠C =7x = 7 x 12° = 84°

Since, all angles are less than 90°, hence the triangle is an acute angled triangle.

Hope it helps :)

Answer 2

Given:-

If the angle of a triangle are in ratio 5 : 3 : 7 than what will be the nature of triangle..

Solution:-

<A + <B +<C=180°

5x+3x+7x=180°

15x=180°

x=180°

x=12°

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5x=5×12=60°

3x=3×12=36°

7x=7×12=84°

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Therefore triangle of 60°,36° & 84° is less than 90° which is called acute triangle,which has 3 acute angles (ie.angles are less than 90°)

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More to learn:-

Triangle[three sides]

m<A + m<B + m<C=180°

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Acute angle: The angle less than 90° is called acute angle.

Right angle: The angle exact 90° is called right angles.

Obtuse angle: The angle more than 90° is called obtuse angle..