# What is a Hypotenuse (Quick, off the Top of Your Head)?
**URL:** https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782
**Category:** In My Humble Opinion
**Created:** [August 9, 2013, 5:06am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782 "2013-08-09T05:06:50Z")
**Posts on this page:** 20
**Page:** 1
### Author:  [@PastTense](https://boards.straightdope.com/u/PastTense)
#### Post date: [August 9, 2013, 5:06am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/1 "2013-08-09T05:06:50Z")
Someone used this is a discussion recently and my immediate reaction was I should know this, knew the general subject area it was used in, but couldn’t recall its definition.
Sometimes it seems amazing I can participate in a discussion forum like Straight Dope as I seem to forgotten almost everything I once knew.
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### Author:  [@Little\_Plastic\_Ninja](https://boards.straightdope.com/u/Little_Plastic_Ninja)
#### Post date: [August 9, 2013, 5:12am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/2 "2013-08-09T05:12:09Z")
The side of a right triangle opposite to its right angle. Yes?
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### Author:  [@Rhiannon8404](https://boards.straightdope.com/u/Rhiannon8404)
#### Post date: [August 9, 2013, 5:14am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/3 "2013-08-09T05:14:20Z")
The side of a right triangle that is opposite the 90° angle.
On preview: what **Little Plastic Ninja** said.
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### Author:  [@Inner\_Stickler](https://boards.straightdope.com/u/Inner_Stickler)
#### Post date: [August 9, 2013, 5:16am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/4 "2013-08-09T05:16:35Z")
I’m with them.
I also remember what SOHCAHTOA stands for and the law of sines.
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### Author:  [@panache45](https://boards.straightdope.com/u/panache45)
#### Post date: [August 9, 2013, 6:10am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/5 "2013-08-09T06:10:44Z")
Yep, so far everyone knows this except the OP.
Oh, and by the way, the scarecrow got it wrong.
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### Author:  [@Dervorin](https://boards.straightdope.com/u/Dervorin)
#### Post date: [August 9, 2013, 7:18am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/6 "2013-08-09T07:18:34Z")
> [@Little\_Plastic\_Ninja](#):
>
> The side of a right triangle opposite to its right angle. Yes?
Yep.
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### Author:  [@Celyn](https://boards.straightdope.com/u/Celyn)
#### Post date: [August 9, 2013, 7:26am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/7 "2013-08-09T07:26:22Z")
I’m late to this but I want to say how thrilled I am that I could remember it too. It is school-exam result time, or so the news keeps saying, so it sometimes makes me wonder if I can remember anything at all from school. Sigh of relief. 😃
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### Author:  [@njtt](https://boards.straightdope.com/u/njtt)
#### Post date: [August 9, 2013, 7:29am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/8 "2013-08-09T07:29:15Z")
The squaw on the hippopotamus is equal to the squaw on the other two hides.
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### Author:  [@Malacandra](https://boards.straightdope.com/u/Malacandra)
#### Post date: [August 9, 2013, 7:32am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/9 "2013-08-09T07:32:56Z")
😃
Fun mathematical fact: Inside any triangle it is possible to draw one and only one circle that just grazes all three sides. If the triangle is Pythagorean (right-angled with whole-number sides) then the radius of the circle is also a whole number.
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### Author:  [@Giles](https://boards.straightdope.com/u/Giles)
#### Post date: [August 9, 2013, 7:50am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/10 "2013-08-09T07:50:36Z")
> [@Malacandra](#):
>
> Fun mathematical fact: Inside any triangle it is possible to draw one and only one circle that just grazes all three sides. If the triangle is Pythagorean (right-angled with whole-number sides) then the radius of the circle is also a whole number.
If the lengths of the three sides of the triangle are a, b and c, where c is the hypotenuse, then the radius is (a + b - c) / 2.
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### Author:  [@Derleth](https://boards.straightdope.com/u/Derleth)
#### Post date: [August 9, 2013, 8:39am UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/11 "2013-08-09T08:39:26Z")
The side opposite the right angle in a right triangle.
Equivalently, any diagonal joining two opposite corners of a rectangle or square.
Also, if you take two orthogonal vectors, lay them tip-to-tail as per standard Euclidean vector addition, the hypotenuse of the resulting right triangle is the vector which results from said vector addition. This plus the Pythagorean theorem justifies the form of the Euclidean metric.
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### Author:  [@Sicks\_Ate](https://boards.straightdope.com/u/Sicks_Ate)
#### Post date: [August 9, 2013, 12:57pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/12 "2013-08-09T12:57:24Z")
Hm, I thought I had it but I was lacking the ‘right triangle’ part. Is there a word for the long end of an obtuse triangle?
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### Author:  [@Waxwinged](https://boards.straightdope.com/u/Waxwinged)
#### Post date: [August 9, 2013, 12:58pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/13 "2013-08-09T12:58:20Z")
A thingie that intercepts a triangle?
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### Author:  [@DrFidelius](https://boards.straightdope.com/u/DrFidelius)
#### Post date: [August 9, 2013, 1:36pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/14 "2013-08-09T13:36:23Z")
> [@njtt](#):
>
> The squaw on the hippopotamus is equal to the squaw on the other two hides.
Sorry, but shouldn’t she be equal to the \*sons \*of the squaws on the other two hides.
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### Author:  [@Shodan](https://boards.straightdope.com/u/Shodan)
#### Post date: [August 9, 2013, 2:20pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/15 "2013-08-09T14:20:33Z")
Is “the longest side of a right triangle” incorrect? I think by definition that is the side opposite the right angle.
Regards,
Shodan
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### Author:  [@Greg\_Charles](https://boards.straightdope.com/u/Greg_Charles)
#### Post date: [August 9, 2013, 2:41pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/16 "2013-08-09T14:41:31Z")
> [@Shodan](#):
>
> Is “the longest side of a right triangle” incorrect? I think by definition that is the side opposite the right angle.
>
> Regards,
> Shodan
The side opposite the right angle is always the longest.
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### Author:  [@gigi](https://boards.straightdope.com/u/gigi)
#### Post date: [August 9, 2013, 3:53pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/17 "2013-08-09T15:53:59Z")
As a quilter designing simple geometric patterns and figuring measurements, I often have mantras like “1, 1, square root of 2” (for the sides of a 45/45/90 triangle) and “1, square root of 3, 2” (for the sides of a 30/60/90 triangle).
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### Author:  [@PookahMacPhellimey](https://boards.straightdope.com/u/PookahMacPhellimey)
#### Post date: [August 9, 2013, 4:07pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/18 "2013-08-09T16:07:12Z")
> [@panache45](#):
>
> Yep, so far everyone knows this except the OP.
Yes, because surely everyone who didn’t know came into the thread especially to say so.
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### Author:  [@Darth\_Panda](https://boards.straightdope.com/u/Darth_Panda)
#### Post date: [August 9, 2013, 4:10pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/19 "2013-08-09T16:10:39Z")
> [@Inner\_Stickler](#):
>
> I’m with them.
>
> I also remember what SOHCAHTOA stands for and the law of sines.
Apparently not, the first law of sines is that we do not talk about sines.
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### Author:  [@Grrr](https://boards.straightdope.com/u/Grrr)
#### Post date: [August 9, 2013, 4:10pm UTC](https://boards.straightdope.com/t/what-is-a-hypotenuse-quick-off-the-top-of-your-head/665782/20 "2013-08-09T16:10:48Z")
Well, I was close. I thought it was the remaining angle when the other two angles were known. If A=90° and B=50° then the unknown angle C would be the hypotenuse (40°).
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