The numbers $\sqrt{2u-1}$, $\sqrt{2u+1}$ and $2\sqrt{u}$ are the side lengths of a triangle. How many degrees are in the measure of the largest angle?
I notice that the side lengths are all related to the same variable, $u$, which means they are not independent. I also notice that they all involve square roots, which makes me think of the Pythagorean theorem. I wonder if the triangle is a right triangle, or if I can use the law of cosines to find the angle. To test the right triangle idea, I square each side length and see if they satisfy the Pythagorean equation: $a^2 + b^2 = c^2$. Squaring each side, I get: $a^2 = 2u-1$, $b^2 = 2u+1$, and $c^2 = 4u$. Adding $a^2$ and $b^2$, I get: $a^2 + b^2 = 4u$. Comparing this with $c^2$, I see that they are equal: $a^2 + b^2 = c^2 = 4u$. This means that the triangle is indeed a right triangle, and the largest angle is the right angle. The measure of a right angle is 90 degrees. 