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

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In summary, the conversation discusses the possibility of solving for three unknown values (a, b, and c) using two equations. The equations provided are a+b+c=180 and tana+tanb+tanc=sq.(3) or tan a tanb tanc=sq.3. The participants suggest using additional equations or constraints and discuss the potential errors or limitations in the original question.
  • #1
m_s_a
88
0
find a,b,c

a+b+c=180

tana+tanb+tanc= sq.(3)
 
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  • #2
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.
 
  • #3
Sure it shouldn't say a+b+c=90?
Because then we could use
[tex] tan(30^{\circ}) = \frac{\sqrt{3}}{3}[/tex]
and get the correct result.
 
  • #4
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).
 
  • #5
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.
 
  • #6
div curl F= 0 said:
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)
??
 

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

How do I find the values of a, b, and c in a quadratic equation?

To find the values of a, b, and c in a quadratic equation, you can either use the quadratic formula or factor the equation. The quadratic formula is (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients in the equation of the form ax^2 + bx + c = 0. Factoring involves finding two numbers that multiply to give you c and add to give you b. Once you have the values of a, b, and c, you can plug them into the quadratic formula to solve for the roots of the equation.

Can I use the quadratic formula to find a, b, and c for any quadratic equation?

Yes, you can use the quadratic formula to find the values of a, b, and c for any quadratic equation. However, if the value inside the square root (b^2 - 4ac) is negative, then the equation has no real solutions. This is because you cannot take the square root of a negative number. In this case, the equation has complex solutions.

What is the purpose of finding the values of a, b, and c in a quadratic equation?

The values of a, b, and c in a quadratic equation are used to determine the shape of the parabola and the location of the x-intercepts or roots of the equation. They can also help in solving real-world problems that involve quadratic relationships, such as finding the maximum or minimum value of a function.

Can I solve a quadratic equation without knowing the values of a, b, and c?

No, you cannot solve a quadratic equation without knowing the values of a, b, and c. These coefficients are essential in determining the roots of the equation. However, in some cases, you can estimate the roots by graphing the equation or using the quadratic formula to find approximate values.

Are there other methods for finding the values of a, b, and c in a quadratic equation?

Yes, other methods for finding the values of a, b, and c in a quadratic equation include completing the square and using the discriminant. Completing the square involves manipulating the equation to get it in the form of (x + p)^2 + q = 0, where p and q are constants. The values of a, b, and c can then be identified from this form. The discriminant is b^2 - 4ac and can be used to determine the nature of the solutions (real or complex) without actually solving the equation.

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