Trigonometric functions problem

AI Thread Summary
The problem involves finding the value of x in a triangle where the base is composed of two segments measuring 8 and 12 units, and the angle relationships are defined using trigonometric functions. The equations tan(Θ) = x/20 and tan(2Θ) = x/8 are established. An attempt to solve leads to the equation x^3 - 80x = 0, which simplifies the problem. A participant points out a mistake in the previous calculations, indicating that an x was lost, which resolves the confusion. The discussion highlights the collaborative nature of problem-solving in mathematics.
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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...
 

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welcome to pf!

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

oooh :cry: …

you lost an x ! :blushing:​
 
...i'm confused :P
 
x3 - 80x = 0 :wink:
 
oooooooooooooooh! great! that fixes everything! thank you!
 

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