Answer
obtuse
Work Step by Step
In an acute triangle, the square of the length of the longest side is shorter than the squares of the lengths of the other two sides; therefore, $c^2 < a^2 + b^2$ or $a^2 + b^2 > c^2$.
In an obtuse triangle, the square of the length of the longest side is longer than the squares of the lengths of the other two sides; therefore, $c^2 > a^2 + b^2$, or $a^2 + b^2 < c^2$.
Finally, in a right triangle, the square of the length of the longest side is equal to the squares of the lengths of the other two sides; therefore, $c^2 = a^2 + b^2$, or $a^2 + b^2 = c^2$.
Let's find out what situation exists for the triangle with the given sides:
$10^2 + 12^2$ ? $16^2$
Evaluate the exponents:
$100+ 144$ ? $256$
Add to simplify:
$244 < 256$
So $a^2 + b^2 < c^2$; therefore, this triangle is an obtuse triangle.
