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The corner of the room is 90 degrees and the front edge of the counter will be 30 inches out from the corner of these two walls. So a triangle with a 90, two 45 corners and i know the 'diameter' is 30. How long are the sides? There must be a simple? formula for that. Thanks

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  • $\begingroup$ hypotenuse ? or some other diameter... $\endgroup$ – user645636 Jan 25 at 22:35
  • $\begingroup$ Why don't you just measure it? $\endgroup$ – Neal Jan 25 at 22:35
  • $\begingroup$ @Neal Sense of humor well appreciated. A rarity these last times... $\endgroup$ – Jean Marie Jan 29 at 19:15
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Something like this?

enter image description here

$30\sqrt 2 \approx 42.4$

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  • $\begingroup$ That's it! I was drawing lines on the cardboard further and further out till i was really close to 42 inches $\endgroup$ – Robert Jan 25 at 22:53
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Yes, there's indeed a formula. The sides are equal to $\frac{1}{\sqrt{2}}$ the diamenter, roughly $21.2$.

Please tell me this is real life question and not an exercise. :)


Since we are not aware of your definition of "diameter", the exact value of the sides is not known... It's possible that the exact value is an element of $\mathbb{Q}[\sqrt{2}]$.

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    $\begingroup$ Are you sure about that? $\endgroup$ – Doug M Jan 25 at 22:39
  • $\begingroup$ Indeed, I'm not sure. $\endgroup$ – BQT Jan 25 at 22:41
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    $\begingroup$ Wife and i really are working on building a counter top for a bathroom sink, mid century modernish lol. Appreciate everyones help Cheers! $\endgroup$ – Robert Jan 25 at 22:55
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    $\begingroup$ Happy to see maths serving the people. $\endgroup$ – BQT Jan 25 at 22:56
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Drawing the 30 inch line that you described, I see it splits your triangular counter into two sub-triangles, each of which is 45-45-90. The lengths of the sides of one of the sub-triangles are 30, 30, and $30\sqrt{2}$.

So the answer is $30\sqrt{2}$.

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  • $\begingroup$ Wow, thanks! ok, so my wife figured out to split it into 2 right angle? triangles giving the one side 30, but we couldn't figure out what to do from there. Thanks for the help! Math is cool! $\endgroup$ – Robert Jan 25 at 22:50

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