Question 1052435
.
What type of triangle (right, obtuse, acute) would the side lengths 6, 13, and the square root of 130 make? Or does it even make a triangle?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
{{{sqrt(130)}}} = 11.4 (approximately).


So, it is between 6 and 13, of course.


You can check that all three "triangle inequalities" for the side lengths of a triangle are in place,
so the triangle does exist with these side lengths.


The 13 units side is longest.
And {{{6^2 + (sqrt(130))^2}}} = {{{36+130}}} = {{{166}}} is less than {{{13^2}}} = 169.

It means that the given triangle is acute.
</pre>