SOLUTION: 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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Question 118270This question is from textbook
: 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. This question is from textbook

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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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.
:
After drawing this triangle out it was apparent that we are given the sin of 30:
:
Side opposite: AC = 6x^2-4x and hypotenuse: AB = 2x
;
%28%286x%5E2+-+4x%29%29%2F%282x%29 = sin(30)
%282x%283x+-+2%29%29%2F%282x%29 = 1%2F2
Cancel out the 2x and you have:
3x - 2 = 1%2F2
3x = 1%2F2 + 2
3x = 1%2F2 + 4%2F2
x = 5%2F2 * 1%2F3
x = 5%2F6
:
:
Check solution using the decimal of (5/6); x = .8333
%28%286x%5E2+-+4x%29%29%2F%282x%29 =
%286%28.8333%5E2%29+-+4%28.8333%29%29%2F%282%28.8333%29%29 =
%28%284.1665+-+3.3333%29%29%2F%281.6667%29 = .500, the sine of 30 degrees