<PRE><B>Question 118270</B>
In triangle ABC, the measure of angle C=90, the measure of angle B=30, AC=6x^2-4x, and AB=2x. Find the value of x.
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After drawing this triangle out it was apparent that we are given the sin of 30:
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Side opposite: AC = 6x^2-4x and hypotenuse: AB = 2x
;
{{{((6x^2 - 4x))/(2x)}}} = sin(30)
{{{(2x(3x - 2))/(2x)}}} = {{{1/2}}}
Cancel out the 2x and you have:
3x - 2 = {{{1/2}}}
3x = {{{1/2}}} + 2
3x = {{{1/2}}} + {{{4/2}}}
x = {{{5/2}}} * {{{1/3}}}
x = {{{5/6}}}
:
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Check solution using the decimal of (5/6); x = .8333
{{{((6x^2 - 4x))/(2x)}}} = 
{{{(6(.8333^2) - 4(.8333))/(2(.8333))}}} = 
{{{((4.1665 - 3.3333))/(1.6667)}}} = .500, the sine of 30 degrees</PRE>