SOLUTION: Can we make a triangle with side lengths: 12, 18, and 16?

Question 530511: Can we make a triangle with side lengths: 12, 18, and 16?
Found 2 solutions by reviewermath, oberobic:
Answer by reviewermath(1029) (Show Source): You can put this solution on YOUR website!
because 18 - 12 = 6 and 18 + 12 = 30 The third side is between 6 and 30, exclusive. So 6 is not possible side if the other 2 sides are 12 and 18.
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Applying the law of cosines:
.
c^2 = a^2 + b^2 - 2*a*b*(cos(x)), where 'x' is the angle between 'a' and 'b'.
.
c^2 - a^2 - b^2 = -2*a*b*(cos(x))
.
(c^2 -a^2 -b^2)/(-2*a*b) = cos(x)
.
(18^2 -12^2 -16^2)/(-2*12*16) = .1979166666666667
.
We can see that .1979166666666667 is a valid value for the cosine function.
.
So, yes, you could have a triangle with sides of 12, 16, and 18.
.
Done.

RELATED QUESTIONS
Can you make a triangle with side lengths: 18, 18, and... (answered by oberobic)
Can you make a triangle with side lengths: 9, 11, and... (answered by Alan3354)
can we make a triangle with 2cm,2cm and... (answered by fcabanski)
A women has a triangular garden with side lengths of 10 m, 12 m and 4 m. Determine the... (answered by josgarithmetic)
What is the lowest whole-number side length (in inches) that would ensure the triangle is (answered by ikleyn,math_tutor2020)
Is a triangle with side lengths of 9 cm, 16 cm, and 25 cm a right triangle? Explain. (answered by Alan3354,josgarithmetic)
is it possible to have a triangle with side lengths of 7,4 and 12 inches long? (answered by solver91311)
is it possible construct a triangle with side lengths 9, 12, and... (answered by Alan3354,jim_thompson5910)
what is the longest side of a triangle with a perimeter of 39 if a similar triangle has... (answered by Alan3354)