Trigonometry and Solve

Question

I'm trying to find values for "x" using Solve, but I do not think it's the best solution. What is the most appropriate function to calculate this?

Solve[Tan[α] == a/x && Tan[2 α] == (a + 5)/x && x^2 + (a + 5)^2 == 10^2, {x, a}]

Solve[Tan[\[Alpha]] == a/x && Tan[2 \[Alpha]] == (a + 5)/x && x^2 + (a + 5)^2 == 100 && 0 < \[Alpha] < Pi/4 && 0 < a < 10 && 0 < x < 10, {x, a, \[Alpha]}] — Feyre, Dec 06 '16 at 12:36

score 2 · Accepted Answer · edited Apr 13 '17 at 12:55

2

Adding to the comments of Feyre

values={a,x,α}/.Solve[Tan[α]==a/x&&Tan[2 α]==(a+5)/x&&x^2+(a+5)^2==100&&0<α<Pi/2&&0<a<10&&0<x<10,{x,a,α}]//N;
a=values[[1,1]]
x=values[[1,2]]
α=values[[1,3]]

a=3 x=6 α=0.463648 rad

edited Apr 13 '17 at 12:55

Community

1

answered Dec 06 '16 at 12:49

LCarvalho

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You can do {a,x,α}={a,x,α}/.Solve[....], or Solve[....] /. Rule -> Set, or Solve[....] /. Rule -> Equal for a display. – corey979 Dec 06 '16 at 13:14
@corey979 to add to your comment, you could use Reduce instead of Solve in this case. – Greg Hurst Dec 06 '16 at 15:41
@LCarvalho "for a display" – corey979 Dec 07 '16 at 10:56

Trigonometry and Solve

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