Question

if the angle of a triangle are in the ratio of 5:3:7 then show that the triangle is an acute angled triangle

Answer 1

Angle sum property of triangle

A + B +C = 180°

Let the angle here be 5x ,3x and 7x

Then ,
5x + 3x + 7x = 180°
15x = 180°
x = 12°

A = 5x = 5×12=65°
B = 3x = 3×12° = 36°
C = 7x = 7× 12 = 84°

Since all the angles are less than 90° , they are acute angles.

Hence proved

✌Hope it helps ✌

Answer 2

Let the angles of the triangle be 5x, 3x and 7x.

Now the sum of the angles of the triangle is 180 degree.

Therefore,

5x + 3x + 7x = 180

15x = 180

x = 12.

Hence the angles are 60 degree, 36 degree and 84 degree.

Therefore, is is an acute triangle.