Question

The angles in a triangle are in the ratio 1 : 2 : 3

Show that the triangle is a right-angled triangle

Answer 1

The angles are 30°, 60° and 90°.

Explanation:

Hint :

• sum of the angles in triangle = 180°.
• The triangle is a right-angled triangle.

Answer:

Let missing angles be
`x`,
`2x`.

As the triangle is right-angled triangle.

`x + 2x + {90}^(o) = {180}^(o)`

`3x = {180}^(o) - {90}^(o)`

`3x = {90}^(o)`

`x = (90 ^(o) )/(3)`

`x = {30}^(o)`

`2x = 30 * 2 \\ = {60 }^(o)`

Check:

• 30° + 60° + 90° = 180°.

Hope it is helpful....

Answer 2

see explanation

Explanation:

sum the parts of the ratio, 1 + 2 + 3 = 6 parts

Divide 180° ( sum of angles in a triangle ) by 6

180° ÷ 6 = 30° ← value of 1 part of the ratio , then

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

The angles in the triangle are 30°, 60°, 90°

Then the triangle is right angled