Is it possible to form a triangle with the given side lengths? 3,4,6

Expert Answers
flbyrne eNotes educator| Certified Educator

Given a triangle with sides a=3, b=4 and c=6 and angles A opposite to side a, B opposite to side b and C opposite to side c, apply the law of cosines to determine angle A.


Substitute 4 for b, 6 for c and 3 for a.



Apply the law of sines to determine angle B


Substitute 0.44 for sin A, 3 for a and 4 for b and solve for `sinB`



Find angle C using: `A+B+C=180`o


Thus it is possible to form a triangle with sides 3, 4 and 6. The angles are A=26.4 degrees, B=36.9 degrees and C=117.7 degrees.

baxthum8 eNotes educator| Certified Educator

In order to determine if a triangle can be formed with 3 sides we must use the Triangle Inequality Theorem.  

Triangle Inequality Theorem states that any side of a triangle must be shorter than the sum of the other two sides.

Let the sides of the triangle be:

a = 3; b = 4; c = 6

This means `b+cgta`  `rArr 4+6 > 3`

`a+b > crArr 3+4>6`

`a+c > brArr 3+6 > 4`

Since these are all true, the lengths of 3,4, and 6 will form a triangle.

amysor | Student

In order to decided wheter the sides given can truly form a triangle, you must use the Triangle Inequality Theorem

You label the 3 sides: side a, side b, side c. It does not matter on which side a, b, or c.

`Delta `     A+B>C



For this example:

We could label this triangle with sides

side a= 3

side b= 4

side c =6

To determine if it is a triangle, you have to see if all the inequalites are true

3+4>6      Correct

4+6>3      Correct

3+6>3      Correct

All sides do fit the Triange Inequality Theorem, therefore, it is possible to form a triangle with these side lengths.

If you have any other questions on this topic. Feel free to contact me. Hope I have helped you.