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QUESTION: Hi,

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.

Thanks,

AL

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

Anne

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

QUESTION: Hi Anne,

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,

AL

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

Not

L^2 + r^2 = a^2

Therefore

a^2 = L^2 - r^2

and

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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