URGENT MATHS HELP! Find the Positive Value

[Guest nadine12]

Could anyone be so kind enough to help me with this question and show me the working so I can understand how you got the answer???

 

I shall have to write the square root as an actual word:

 

square root b squared - c squared, find the positive value of b given a=5.6 and c=4.4.

 

Thankyou ever so much.

 

Nadine

[JaKiri]

You've missed off how a relates to b and c.

[zaphod]

assuming that a = "square root b squared - c squared", then

 

b = square root of 12

[violetendncy]

Nadine:

 

I assume you meant : "the square root of a quantitiy equal to B squared minus C squared as a positive real number"

 

I may be mistaken if you wanted : "the difference of the square root of a quantity equal to B squared with a quantity equal to C squared."

 

With that in mind, I press on...hopefully not in vein!

 

The key to understanding this is Pythagoras. That wiley Grecian stated (per your modus operandi) " 'A' squared plus 'B' squared is equal to 'C' squared".....if 'A' and 'B' are the legs of a right triangle (arbitrary in order) and 'C' is the hypotenuse(the one characteristic longest side) of that right triangle. Thus, we've:

 

"XX" meaning X times X, or X squared...

"sqrt()" meaning the square root of whatever is inside the parentheses...

 

(CC) = (AA) + (BB)

 

C = sqrt( (AA) + (BB) )

 

Which finds the hypotenuse side length.

 

In order for us to get something like what you got, we need to be looking for the magnitude (value or length size) of a LEG, rather than the HYPOTENUSE. Thus thinking, we make the following:

 

(CC) = (AA) + (BB)

 

(CC) - (AA) = (BB)

 

taking a root for the solution of B (one of the legs);

 

sqrt( (CC) - (AA) ) = B.

 

Now, you mentioned that you wanted the positive solution for B. It should then be noted that the only way for the square-root of a number to be negative is if you are finding some "complex solution".....meaning you are dealing with imaginary numbers. Assuming you want REAL SOLUTIONS for B, you must understand that C squared must be greater than A squared. Ostensibly, you might think that is a BIG limitation on the whole formula, however realize please (and fret not) that you can choose which value is C and which is A. In short, make absolutely certain that you make C the hypotenuse ALWAYS, because in order for you to call it the hypotenuse in the first place, you must observe it to be the longest side of the right triangle in question.

 

To answer your question numerically, we make:

 

B = sqrt( 31.36 + 19.36 ) = sqrt( 50.72 ) =>> 7.1217975259059422378186235125897.....ad nausaem

[ydoaPs]

hold on, is it.

 

[math]\sqrt{b^2-c^2}[/math]

or

[math]\sqrt{b^2}-c^2[/math]

 

and how does any of this relate to a?

 

edit:

here is something cool about the pythagorean theorem:

 

pythagorean theorem-[math]c^2=a^2+b^2[/math]

law of cosines-[math]c^2=a^2+b^2-(2ab)cos(\gamma)[/math]

 

put in [math]2\pi[/math] for [math]\gamma[/math], and the law of cosines becomes the pythagorean theorem.

[violetendncy]

I'm right....just look o'er my answer.

 

It has to be the sqrt(bsquared minus csquared), and not [b minus csquared] because otherwise it's just addition and root-extraction...and i assume Nadine wasn't confused about that.

 

it's all set equal to a......

[Primarygun]

Not putting [Math] \gamma = \pi/2? [/Math]

[violetendncy]

Oh, I don't mean to seem contrapuntal....I was a little confused on the original question myself, and so I was merely confirming my findings initially.

 

As for the gamma stuff, I really don't know enough about it to make any sort of intelligent comment. Lol. I'm sure you're probably right, though.