Trigonometric functions problem

[luludatis]

Homework Statement

Find x

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

Homework Equations

tan$$\Theta$$ = opp/adj
tan 2$$\Theta$$ = 2tan/1-tan²

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]

welcome to pf!

hi luludatis! welcome to pf!

320x=400x-x³
x³-80=0

oooh …

you lost an x ! ​

 

[luludatis]

...i'm confused :P

 

[tiny-tim]

x³ - 80x = 0

 

[luludatis]

oooooooooooooooh! great! that fixes everything! thank you!