# Hi, i am trying to put in a sink in the corner of the bathroom

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

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

Something like this? $$30\sqrt 2 \approx 42.4$$

• That's it! I was drawing lines on the cardboard further and further out till i was really close to 42 inches – Robert Jan 25 at 22:53

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 $$\mathbb{Q}[\sqrt{2}]$$.

• Are you sure about that? – Doug M Jan 25 at 22:39
• Indeed, I'm not sure. – BQT Jan 25 at 22:41
• Wife and i really are working on building a counter top for a bathroom sink, mid century modernish lol. Appreciate everyones help Cheers! – Robert Jan 25 at 22:55
• Happy to see maths serving the people. – BQT Jan 25 at 22:56

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 $$30\sqrt{2}$$.

• 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! – Robert Jan 25 at 22:50