Question 550578
<font face="Times New Roman" size="+2">


The largest side being twice the smallest makes the triangle a candidate to be a 30-60-90 right triangle.  The largest angle being thrice the smallest clinches it:  90 is three times 30.


The sides of a 30-60-90 right triangle are in proportion *[tex \Large 1:\frac{\sqrt{3}}{2}:\frac{1}{2}].  Since it is a right triangle, one of the legs is the base and the other leg is the altitude.  Hence, a 30-60-90 right triangle with a hypotenuse of 1 would have an area of *[tex \Large \frac{\frac{\sqrt{3}}{2}\,\cdot\,\frac{1}{2}}{2}\ =\ \frac{\sqrt{3}}{8}].


So


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\left(\frac{\sqrt{3}}{8}\right)\ =\ 32\sqrt{3}]


Solve for *[tex \Large x]


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>