Sorry for coming up with a "do-it-for-me"-question, but I can't think of another way to get help with manually solving the following system of four equations:

  1. $50=x*\cos(\beta)-y*\cos(\alpha)$

  2. $0=x*\sin(\beta)-y*\sin(\alpha)$

  3. $0=x*\sin(\gamma)+y*\cos(\alpha)$

  4. $45=x*\cos(\gamma)-y*\sin(\alpha)$

$x$, $y$, $\beta$ and $\gamma$ are unknown.

$\alpha$ is a known constant with the given value of $63.5°$.

I tried all approaches I could think of and always got stuck on one equation with two unknown angels, for example $50\tan\beta*(\sin\alpha\tan\gamma+\cos\alpha) = 45\tan\gamma*(\cos\alpha\tan\beta-\sin\alpha)$.

EDIT: This is the numerical solution of WolframAlpha, but, as stated above, I need to do it manually.



1 Answer 1


In all the equations move the y term to the LHS. Square the first two equations and add. Use Sin^2 + Cos^2=1. So have equation for x^2 & terms in y & y^2. Do the same with 3rd & 4th equations. Eliminate x^2 from the resultant equations to give quadratic in y which you can solve. From here you have x and so on and so on.

  • $\begingroup$ Squaring makes sense, thanks a lot! $\endgroup$
    – MaxD
    Feb 4, 2015 at 13:30

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.