Question

The angles in a triangle are in the ratio 1:2:3
work out these three angles

Answer 1

smallest angle = 30

medium angle = 60

largest angle = 90

This is a 30-60-90 right triangle

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Work Shown

x = some positive real number

1x = smallest angle

2x = medium angle

3x = largest angle

The ratio 1x:2x:3x reduces to 1:2:3 when you divide all parts by x, which shows the angles are in the proper ratio.

For any triangle, the three angles always add to 180.

1x+2x+3x = 180

6x = 180

x = 180/6

x = 30

smallest angle = 1x = 1*30 = 30

medium angle = 2x = 2*30 = 60

largest angle = 3x = 3*30 = 90

This is a 30-60-90 right triangle.

Answer 2

30:60:90

m<1 = 30

m<2 = 60

m<3 = 90

Explanation:

triangle = 180 degrees

1:2:3 = 6 parts

180/6 = 30

1 x 30 = 30

2 x 30 = 60

3 x 30 = 90

30:60:90