Programming Challenge: a classic trigonometry problem

[Thomas Klemm]

(01-01-2014 06:12 AM)RMollov Wrote:  It's only one equation and HP48 finds the solution in no time.

I used these these two equations with the Multiple-Equation Solver:
\[
\frac{\sqrt{a^2-x^2}}{x}=\frac{c}{x-d} \\
\frac{\sqrt{b^2-x^2}}{x}=\frac{c}{d} \\
\]
But the HP-48 can't deal with it. What about HP-50G?

However I used additional variables:
\[
u=\sqrt{a^2-x^2} \\
v=\sqrt{b^2-x^2} \\
\]
And then reversed nominator and denominator:
\[
\frac{x}{u}=\frac{x-d}{c} \\
\frac{x}{v}=\frac{d}{c} \\
\]
Adding these two equations leads to:
\[
\frac{x}{u}+\frac{x}{v}=\frac{x-d}{c}+\frac{d}{c}=\frac{x}{c}
\]
Now we can get rid of \(x\):
\[
\frac{1}{u}+\frac{1}{v}=\frac{1}{c}
\]
In a similar way I could remove \(x\) from the first two equations and got:
\[
u^2-v^2=a^2-b^2
\]
Your solution is correct. Congratulations!

Cheers
Thomas