Multiple answers from solve

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AB=180
AO=60
BO=200

syms alpha

eqn1 = BO^2 == AB^2+AO^2-2*AB*AO*cosd(alpha)

eqn2 = solve (eqn1,alpha)
vpa(eqn2)

ans =

259.32807071423785412135760253313

100.67192928576214587864239746687

I know that it's the latter (100.6719....), but why does it give me 2 answers and how do I make matlab give me 1 answer?

Answer 1

[Walter Roberson]

AB=180

AB = 180

AO=60

AO = 60

BO=200

BO = 200

syms alpha

eqn1 = BO^2 == AB^2+AO^2-2*AB*AO*cosd(alpha)

eqn1 = 

sol = solve(eqn1, alpha)

sol = 

vpa(sol)

ans = 

How is MATLAB to know that one of the solutions is more right than the other?

You could vpasolve() with a range:

vpasolve(eqn1, alpha, [0 180])

ans = 

100.67192928576214587864239746687

[Kevin]

So does that mean that there are 2 possible answers for alpha? I'm sorry if this sounds dumb, because I've just started using Matlab.

[Walter Roberson]

Yes, it means thare are two possible answers for alpha.

AB=180

AB = 180

AO=60

AO = 60

BO=200

BO = 200

syms alpha

eqn1 = BO^2 == AB^2+AO^2-2*AB*AO*cosd(alpha)

eqn1 = 

sol = solve(eqn1, alpha)

sol = 

vpa(sol)

ans = 

Now let us back-substitute the solutions into the defining equation

subs(eqn1, alpha, sol)

ans = 

lhs(ans) - rhs(ans)

ans = 

The difference between the two sides is 0, for both answers. So both answers are solutions. And MATLAB has no reason to know that one is "right" for your situation unless you give it more information to tell it which one you prefer.

[Kevin]

Thank you so much.