Where the diagonals intersect several things occur. 4 right angles result from this, and they bisect each other. If XZ is 10, then XV is 5. The angle XYV then will be used as the reference angle (30), the side across from it is XV=5, and the side adjacent VY, is the one we are looking for. We will use the tangent ratio, since that is the one that relates the reference angle to the side opposite and the side adjacent. Therefore, [tex]tan(30)= \frac{5}{VY} [/tex] and [tex]VY= \frac{5}{tan30} [/tex]. That means that segment VY = 8.66, which, if you're using your Pythagorean triples, is equal to [tex]5 \sqrt{3} [/tex]. The side across from the 30 angle is x, the side across from the 60 angle is [tex]x \sqrt{3} [/tex]. We know that the side across from the 30 angle is 5, therefore the side across from the 60 angle is [tex]5 \sqrt{3} [/tex]. If you put that into your calculator, you'll get the value that I gave you in decimal. Same thing, just a different way of expressing it.
