Discover the Formula for 180 Degrees with Tana, Tanb, and Tanc

[m_s_a]

find a,b,c

a+b+c=180

tana+tanb+tanc= sq.(3)

 

[div curl F= 0]

Not too sure if this is solvable in general as you only have 2 equations but 3 unknowns. Are there any other equations/constraints that you didn't post up?

Generally, you need n equations/constraints to solve for n unknowns.

 

[J.D.]

Sure it shouldn't say a+b+c=90?
Because then we could use
tan(30^{\circ}) = \frac{\sqrt{3}}{3}
and get the correct result.

 

[MathematicalPhysicist]

J.D you could also ask shouldn't it be a+b+c=180 and tg(a)+tg(b)+tg(c)=3sqrt3, cause we can use: tg(60)=sqrt(3).

 

[J.D.]

That also makes sense. I really feel that there is something wrong with the original question and have my doubts whether or not there even exist a solution. I have to admit though that I haven't made any serious attempts to prove it.

 

[m_s_a]

Not too sure if this is solvable in general as you only have 2 equations but 3 unknowns. Are there any other equations/constraints that you didn't post up?

Generally, you need n equations/constraints to solve for n unknowns.

A theory can be used
Is

if
a+b+c=180
then tanget a + tanget b + tanget c = tan a tanb tanc


1)
tanget a + tanget b + tanget c = sq.3
2)
tan a tanb tanc= sq.3
3)
??