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I sent a question that had a .com footnote,
I think the .com blocks it from my inbox.
Could you please resend it to me without that .com in the text.


ANSWER: Hi Al, I will be happy to assist you.

First I assume capital A is a different variable than the lower case a you want to solve for.

Because L^2 + r^2 = a^2, taking the square roots of both sides gets
a = sqrt(L^2 + r^2)

what is also known is r= L x Ac/G
substituting this in gets

a = sqrt(L^2 + (L x Ac/G)^2)

Squaring L x Ac/G gets

a = sqrt(L^2 + L^2 x (Ac)^2/G^2)

Factoring out the L^2 and taking the square root of it gets
a = Lsqrt(1 + (Ac)^2/G^2)

I'm keeping Ac in parenthesis because I am unsure if it is one variable or two

1 can be rewritten as G^2/G^2 so the denominator of G^2 can be factored out, and square rooted to get
a = (L/G)sqrt(G^2 + (Ac)^2)

Please let me know if you are unsure how I got this.

I hope this helps


---------- FOLLOW-UP ----------


Bad news, here's why;

G = 9.80175174
L = 7
Ac = .17234849511725
r  = .12308406678955

r  =  L  x  Ac  /  G

Right angle triangle;
Hypotenuse = L = 7
r  = .12308406678955
unknown side =  "a"

Your equation;

a = (L/G)sqrt(G^2 + (Ac)^2)

I get an answer for  "a"  to be   7.00108

But via Pythagoras we know that  "a"  truly equals  6.99891779580976

Anne can you please tell me why the new equation doesn't give a correct result.

It's very important.

Thank you very much for your assistance,

Hi Al, if L is the hypotenuse and r and a are the legs of a right triangle then

a^2 + r^2 = L^2
L^2 + r^2 = a^2


a^2 = L^2 - r^2


a = (L/G) x sqrt(G^2 - (Ac^2))

I hope this helps.
If there is still an error, please let me know what the variables stand for and I may be able to help.


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Anne Losch


Solving equations, graphing, evaluatin equations, factoring, functions, systems of equations, rational equations, exponent, complex numbers, word problems, logarithms, polynomials, and all topics in an Algebra 1, Algebra 2, or College Algebra class


I have a teaching certificate, I have taught Algebra 1 & 2 as well as tutored those subjects and tutored in College Algebra.

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