Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to fill in the circles of a triangle. The sum of the numbers on each side of the triangle is equal to the length of that side. What is the triangle with the largest (or smallest) angle measure that you can make?

### Hint

The smallest interior angle of a triangle is always opposite the shortest side

The largest interior angle of a triangle is always opposite the longest side

### Answer

Side A: 6+8+9+7=30 Side B: 7+4+1+3=15 Side C: 3+2+5+6=16

Angle A: 150.799 Angle B: 14.119 Angle C = 15.082

A triangle with the smallest angle (there are several variations with the same angle):

Side A: 1+2+3+4=10 Side B: 4+8+9+7=28 Side C: 1+5+6+7=19

Angle A: 10.844 Angle B: 148.212 Angle C = 20.944

Source: Erick Lee

Is this item titled incorrectly?

It is not using the law of cosines is it?

Isn’t it just using the triangle inequality theorem?

Ignore above comment. Sorry