What is a Hypotenuse (Quick, off the Top of Your Head)?

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.

The side of a right triangle opposite to its right angle. Yes?

The side of a right triangle that is opposite the 90° angle.

On preview: what Little Plastic Ninja said.

I’m with them.

I also remember what SOHCAHTOA stands for and the law of sines.

Yep, so far everyone knows this except the OP.

Oh, and by the way, the scarecrow got it wrong.

Yep.

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. :smiley:

The squaw on the hippopotamus is equal to the squaw on the other two hides.

:smiley:

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.

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.

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?

A thingie that intercepts a triangle?

Sorry, but shouldn’t she be equal to the *sons *of the squaws on the other two hides.

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.

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).

Yes, because surely everyone who didn’t know came into the thread especially to say so.

Apparently not, the first law of sines is that we do not talk about sines.

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°).