Area of a right-angled triangle

[oen_maclaude]

yes i do understand now.

(to chroot) however, the fact that the possibility that a certain triangle of .such dimension will be existing only that the height is not perpendicular to the hypotenuse

 

[chroot]

Originally posted by oen_maclaude
only that the height is not perpendicular to the hypotenuse

Right -- and what good is that? That isn't the problem at hand.

- Warren

 

[curiousbystander]

I apologize if I'm intruding, but there must be some important distinction I'm missing. I would appreicate it if somebody would clarify for me. I'm working with these definitions and ideas:

A right triangle is a triangle with a right angle (90 degrees)

The hypotenuse of a right triangle is the side opposite the right angle

The two remaining sides are called legs.

Either of the legs may arbitrarily be called the base, and then the length of the remaining leg is called the height (customarily the base is drawn horizontally and as the other leg is at a 90 degree angle, the other leg is drawn vertically, again, by custom we draw this leg so that it leaves the corner of the right angle by traveling up-- thus the height coincides with our usual idea of height)

Any triangle drawn in a circle with one edge forming the diameter of aforesaid circle is a right triangle, and further, the hypotenuse is the diameter, and the opposite angle is the right angle.
Imagine you have such a circle/triangle... by moving the pt that corresponds to the right angle closer and closer to either of the endpts you create a triangle with one very short leg and one leg that is arbitrarily close the length of the hypotenuse... by rotating the circle and the inscribed triangle we can make that long edge correspond to the height, so the restriction on the height is that the height may not be equal to (or longer) then the hypotenuse.

The ratio of edges on a 45,45,90 triangle is not 1 to 1 to 2 since 1^2 + 1^2 is not 2^2 It is 1 to 1 to sqrt(2).

I think that's everything... of course I'm assuming we're doing all this on a flat surface... all bets are off if we're on some two manifold.

 

[chroot]

curiousbystander,

I'm not sure I saw any question in your post. Please read NateTG's post carefully.

- Warren

 

[oen_maclaude]

yup! i agree with chroot! look back to what NateTG's post. but is was just ok that you really just dropped by to give us your insights.

 

[curiousbystander]

Ooops... sorry about that...What I hadn't been seeing was how NateTG's post ruled out a height of 6... but *slaps forehead* now I see my problem. When NateTG said "A triangle with hypotenuse of 10 can't have a height of 6..." he was referring to the distance from the hypotenuse to the right angle... NOT the length of one of the sides... (that was bothering me). He even came right out and said it in the previous sentence when he used the word altitude... I read the rest of the post several times, and in great detail (and puzzlement), but should have been more thorough. My faith in humanity (and physicists) is restored. :) (although I personally feel quite silly). Thanks.