#### Bailey232008

##### New member

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The only information provided is what you see in the picture. Solve by any means necessary...

- Thread starter Bailey232008
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The only information provided is what you see in the picture. Solve by any means necessary...

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\(\displaystyle A=22.5\sqrt{(R+22.5)(R-22.5)}\)

We also know:

\(\displaystyle A=22.5(R-5)\)

This implies:

\(\displaystyle \sqrt{(R+22.5)(R-22.5)}=R-5\)

Solving this, we find:

\(\displaystyle R=53.125\)

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Please look at this webpageI’ve been working on this for too long. I almost posted this in the Odds and Ends section because I think it’s going to entail more than just geometry. Give this one a shot. Could be a fun challenge for you vets out there if it’s even possible. If you want the back story behind how I came up with it let me know.

The only information provided is what you see in the picture. Solve by any means necessary...View attachment 20083

On it we see \(R=\dfrac{c^2}{8h}+\dfrac{h}{2}\)

From the above diagram \(c=45'~\&~h=5'\).

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You lack the interior angle, so this method doesn’t workDraw a line from where it says 45 to the center of the circle. This gives you a right triangle. What are the lengths of the three sides of this right triangle. Now ask Pythagorous for help.

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Mark and Pka,

great stuff, appreciate the help

great stuff, appreciate the help

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You misunderstood Jomo's suggestion, which doesn't use any angles. In fact, this is how the formula pka gave is derived!You lack the interior angle, so this method doesn’t work

The sides of the triangle are r-h, c/2, and r (the hypotenuse), and solving the Pythagorean theorem for r yields the formula.

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As already mentioned Pythagorous' theorem does not use angles. you have the 3 sides of the right triangle in terms of R. What seems to be the problem?You lack the interior angle, so this method doesn’t work

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Why couldn't you use the 45You lack the interior angle, so this method doesn’t work