Trigonometric functions problem

[luludatis]

1. The problem statement, all variables and given/known data
Find x

base of triangle: 2 pieces, 8+12
opposite end: x
angle: \Theta ; angle formed by triangle of 8 units and x : 2\Theta


2. Relevant equations
tan\Theta = opp/adj
tan 2\Theta = 2tan/1-tan2

3. The attempt at a solution
tan\Theta= x/20
tan 2\Theta = x/8

x/8=tan2\Theta= 2(x/20) / 1-(x/20)2

(2x/20) / ((400-x2)/400) = 40x/400-x2

x/8=40x/400-x2

320x=400x-x3
x3-80=0


and now I'm stuck. I want to use difference of cubes, but i feel it is getting too complicated...

[tiny-tim]

hi luludatis! welcome to pf! :smile:
320x=400x-x3
x3-80=0

oooh :cry: …

you lost an x ! :blushing:

[luludatis]

...i'm confused :P

[tiny-tim]

x3 - 80x = 0 :wink:

[luludatis]

oooooooooooooooh!!!!! great! that fixes everything!! thank you!!