## Geometry: Common Core (15th Edition)

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.