Question

the angles of a triangle ABC are in the ratio 1:1:2, then the ratio of their sides is

Answer 1

let the sides be x
so, 1x+1x+2x - 180
4x - 180
x- 180/4
therefore x- 45
so the ratio of there sides is 45.....

Answer 2

Given - Ratio of angles

Find - Ratio of sides

Solution - The ratio of the sides of the triangle is 1/✓2:1/✓2:1.

Ratio and angles and the ratio of sides of the triangle are related to each other by the formula -

Side = sine of the angle

Now, as per the fact, the sum of all the angles is 180°.

Let the angles be 1x, 1x and 2x.

Forming mathematical expression -

1x + 1x + 2x = 180

4x = 180

x = 45°

So, the three angles of the triangle are 45, 45 and 90.

Now, side A = sin 45

Side A = 1/✓2

Side B = sin 45

Side B = 1/✓2

Side C = sin 90

Side C = 1

The ratio of the sides of the triangle is 1/✓2:1/✓2:1.