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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.
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.
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
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.
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