math question

[cecilia87]

<p>ImageShack&#174</a>; - Online Photo and Video Hosting</p>

<p>how do you solve this without trig functions such as sin, cos, and tan?</p>

<p>I couldn't figure out any other way to solve this without these trig formulas! (SOHCAHTOA)</p>

[rutgershopeful]

<p>Use the 30-60-90 rule.</p>

<p><a href=“http://upload.wikimedia.org/wikipedia/commons/1/15/Triangle_30-60-90_rotated.png[/url]”>http://upload.wikimedia.org/wikipedia/commons/1/15/Triangle_30-60-90_rotated.png&lt;/a&gt;&lt;/p&gt;

<p>since ABE is an equilateral triangle, then each angle is 60 degrees.
this means angle CBE is 90-60 = 30 degrees.
then use the formula from there You know angle C is 90 degrees, so angle BEC must be 60 degrees.</p>

[teteatete]

<p>Let’s have a look at triangle BCE.
BC = 9;
Recall that the side opposite 60 degrees can be expressed as x*sqrt(3);
The 30 degree side is x and the 90 degree side is 2x;
x = 9/sqrt(3);
AE = 2x = 18/sqrt(3);
AE + BE = 2(18/sqrt(3)); AE and BE are equal.
= 36/sqrt(3);</p>

<p>That simplifies to: 12<em>sqrt(3);
The answer is (C) 12</em>sqrt(3);</p>