Thread: Right Triangles

Right triangles are characterized by their unique angle measures: they contain one RIGHT ANGLE, of course.

Their look is also very unique- they like all triangles own three sides, but one is quite flagrantly longer than the others, and is always OPPOSITE the right angle. This side is called the HYPOTENUSE, the two remaining shorter sides are called LEGS.

This brings us to the PYTHAGOREAN THEOREM. This theorem states that the sum of the squares of the lengths both legs must equal the square of the length of the hypotenuse. This is better stated as A SQUARED PLUS B SQUARED EQUALS C SQUARED, Where A and B are the two legs and C is the hypotenuse.

So, if I have a triangle with one leg measuring 2, and another measuring 3, what is the length of the hypotenuse?

Simple!

NOTE: (2) denotes a two in superscript.

A(2) + B(2) = C(2)

2(2) + 3(2) = C(2)

4 + 9 = C(2)

11 = C(2)

RADICAL 11 = C

Okay, maybe not so simple, but hey, we got a solution!

There are also SPECIAL RIGHT TRIANGLES (though I think they're all special). These are the 45-45-90 and 30-60-90 Triangles.

Each number up above denotes an angle measure, so a 45-45-90 triangle has two 45 degree angles and a 30-60-90 triangle has a 30 degree angle, a 60 degree angle, and it's 90 degree angle.

First, 45-45-90 triangles.

Really, all you need to know is that each leg is CONGRUENT, which means that they measure the same length and are not merely similar, but copies as well. (See article "CONGRUENCY", should I make it). Also, to easily find the length of the hypotenuse, simply multiply the length of one leg by RADICAL 2. Remember, RADICAL means "the square root of" for a number that has no square root.

Now, 30-60-90 triangles.

You need the shorter leg to do anything with these triangles! The shorter leg doubled is the length of the hypotenuse, and the shorter leg multiplied by RADICAL 3 is the length of the longer leg.

And that's that!

I hope you enjoy having fun with right triangles!

[Author's Note: I love them so much!]

Woot. Did you just randomly decide to write about right triangles, or was this for something?

Random. I like right triangles.

Ha, cool.