Cosine Rule

math_struggler

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May 27, 2014
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I'm having trouble with where to start. I tried to find the value of x by using the cos rule with 6/x but I'm unsure of how I would apply the cosine to derive the following equation.

Untitled.jpg

The diagram shows the triangle ABC in which angle A = pi/6
AB = 6cm and BC = 4cm
Let AC = xcm


a) Use the cosine rule to derive x2 - 6sqrt(3)x + 20 = 0
b) Use the quadratic formula to show AC has length 3sqrt(3) - sqrt(7) or 3sqrt(3) + sqrt(7)

Though, I'm sure if I had help figuring out (a) I would more than likely be able to solve (b).

Here's to hoping!
Thanks ;)
 
Use Law of Cosines this way:
BC^2 = AB^2 + AC^2 - 2*AB*AC*COS(30)
So:
4^2 = 6^2 + x^2 - 12x[SQRT(3)/2]

That's all you get...we don't do full homework...


I wasn't looking for my homework to be completed by strangers. I realise that this site is for compilation of ideas on how to solve math problems per se. Hence, I should have most likely been clearer about what I was really looking for. What I am having trouble understanding is that once I have found x using the cosine rule in question (a) with the given equation, do I just substitute in the x to determine whether the equation does equal zero? I'm more or less just having trouble understanding the questions. That's all.
Cheers anyways.
 
...once I have found x using the cosine rule in question (a) with the given equation, do I just substitute in the x to determine whether the equation does equal zero?
I don't understand what you're asking here. How do you propose to "find x using the cosine rule" without actually solving the equation? You'll solve that equation by leaving the left-hand side set equal to zero. So what do you mean by "determining whether the equation[sic] does equal zero"? ;)
 
I don't understand what you're asking here. How do you propose to "find x using the cosine rule" without actually solving the equation? You'll solve that equation by leaving the left-hand side set equal to zero. So what do you mean by "determining whether the equation[sic] does equal zero"? ;)
I was only asking for clarification with the questions. It's ok. I've solved it. Thanks.
 
Problem has two solutions:


Triangle side |AC|=7.842 and side |AC|=2.55, see calculation and triangle pictures:

http://www.triangle-calculator.com/?what=ssa&a=6&b=4&b1=30&submit=Solve



Geometrically you can draw this two triangles:

1. draw angle A = pi/6
2. point B - end of line segment |AB|
3. circle from point B with radius |BC|
4. unknown points C is intersect of circle and one leg of angle A. (two insersect, two solutions)
 
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