SOLUTION: I am laying out a peice of furniture and wish to make a pattern. I wish to know the radius of a circle that will subtend a cord of 30 " with a height of 2 1/2". I am 73 and

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Question 16472: I am laying out a peice of furniture and wish to make a pattern.
I wish to know the radius of a circle that will subtend a cord of 30 " with a height of 2 1/2".
I am 73 and took geometry in 1947 - I seem to have forgotten the formulas.
Thanks,
Wyatt Shorter
Found 2 solutions by Earlsdon, rapaljer:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
HI Wyatt, here's a formula that could help solve your problem. If you're interested, it came out of a math tables book (CRC Standard Mathematical Tables) which I have used since the early fifties in college.
C+=+sqrt%284h%282R+-+h%29%29
Since you know C (the chord length) and h (the length of that part of the radius between the chord and the circumference), you can, with a little algebraic manipulation, solve for R, the radius.
C+=+sqrt%284h%282R+-+h%29%29 Square both sides.
C%5E2+=+4h%282R+-+h%29 Divide both sides by 4h.
C%5E2%2F4h+=+2R+-+h Add h to both sides.
%28C%5E2%2F4h%29+%2B+h+=+2R Finally, divide both sides by 2.
%28%28C%5E2%2F4h%29+%2B+h%29%2F2+=+R This can be simplified a bit.
R+=+%28C%5E2+%2B+4h%5E2%29%2F8h
Now let's plug in your values of C (30") and h (2.5") and grind away.
R+=+%2830%5E2+%2B+4%282.5%29%5E2%29%2F8%282.5%29
R+=+%28900+%2B+4%286.25%29%29%2F20
R+=+%28925%29%2F20
R+=+46.25 inches.

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Very interesting problem. I think I might be able to help with this one. I'm sure you have it drawn up with the cord of 30" and a radius at the end of each cord. The radius is the unknown, say x, for this problem. Now, in addition to drawing the radius of x from the center of the circle to each endpoint of the cord, draw another radius right up the middle that will be perpendicular to the cord. That will also be of length x, and it should illustrate the height that you want of 2.5 inches. This radius up the middle also gives you two right triangles, that will allow you to use the Theorem of Pythagoras to solve. In each of these right triangles, the hypotenuse is the radius which is x, and one of the legs will be half of the length of the cord, which is 15. The other leg of the triangle is just below the 2.5 inch height, and it's distance from the center of the circle is the length of the radius x minus the 2.5.

So, do you see the right triangle and what the three sides are? The legs are (x-2.5) and 15, and the hypotenuse is x.

Theorem of Pythagoras: +a%5E2+%2B+b%5E2=+c%5E2 so
+%28x-2.5%29%5E2+%2B+15%5E2+=+x%5E2
+x%5E2+-+5x+%2B+6.25+%2B+225+=+x%5E2

Subtract x^2 from each side and combine the numbers together:
-5x+%2B+231.25+=+0
231.25+=+5x
x=+231.25%2F5+=+46.25 inches

I hope this is correct!! Does it look right? You should probably try this out to see if it really works before you make anything expensive with it. It's a great application to answer the question we hear so often, "What good is math???"

R^2 at SCC