Question 246874
<font face="Garamond" size="+2">


There are a couple of ways to go about this.


First thing you could do is recognize that a 45 45 90 triangle is an isosceles right triangle.  That means that both legs are the same length.  Use the Pythagorean theorem:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sqrt{(5\sqrt{2})^2\ +\ (5\sqrt{2})^2}\ = \sqrt {50\ +\ 50}\ =\ \sqrt{100}\ =\ 10]


Or you could remember that the sides of a 45 45 90 triangle are always in proportion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1:1:\sqrt{2}]


So just multiply by *[tex \LARGE \sqrt{2}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 5\sqrt{2}\,\cdot\,\sqrt{2}\ =\ 5\,\cdot\,2\ =\ 10]



John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>