MaplePrimes - answers and comments on Question, Does this system of equations have no solutions?

there are only 2 variables, but 3 equations,

zsy312 — Sat, 10 Nov 2012 21:57:47 Z

there are only 2 variables, but 3 equations, and when I delete one of the equations for 3 times using fsolve, the result is different.

Solution

Kitonum — Sat, 10 Nov 2012 22:19:12 Z

restart:

a:=3:

eq1:=(a^2+b^2-c^2)/(2*a*b):

eq2:=(b^2+c^2-a^2)/(2*b*c):

eq3:=(c^2+a^2-b^2)/(2*a*c):

solve([eq1=convert(cos(15*Pi/180), radical), eq2=cos(30*Pi/180), eq3=cos(135*Pi/180)], [c,b]);

Thank you very much.

toandhsp — Sun, 11 Nov 2012 04:22:45 Z

Thank you very much.

Re solution

toandhsp — Sun, 11 Nov 2012 07:28:05 Z

When I found the length of sides b and c, I created a triangle satisfies the conditions stated and test the measure of the angles of this triangle. I tried

> restart:

a:=3:

eq1:=(a^2+b^2-c^2)/(2*a*b):

eq2:=(b^2+c^2-a^2)/(2*b*c):

eq3:=(c^2+a^2-b^2)/(2*a*c):

sol:=solve([eq1=convert(cos(15*Pi/180), radical), eq2=cos(30*Pi/180), eq3=cos(135*Pi/180)], [b,c]);

with(geom3d):

point(o,0,0,0):

point(A,a,0,0):

sys:=solve([x^2+y^2=(rhs(op(1,sol[1])))^2,(x-a)^2+y^2=(rhs(op(2,sol[1])))^2],[x,y]);

point(B,rhs(op(1,op(1,sys))),rhs(op(2,op(1,sys))),0):

triangle(T,[o,A,B]):

map(coordinates,DefinedAs(T));

FindAngle(o,T);

FindAngle(A,T);

FindAngle(B,T);

But I don't receive the angles 15 degrees, 30 degrees and 115 degrees directly. How do I tell Maple to do that?

Re

Kitonum — Sun, 11 Nov 2012 22:23:09 Z

In the last three lines add simplify command. You get the angles in radians. Translate to degrees can yourself or by convert command.

Thank you very much.

toandhsp — Mon, 12 Nov 2012 05:24:05 Z

Thank you very much.