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Special Right Triangles 1973 Views


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Transcript

00:05

Right and Special Right Triangles, a la Shmoop. Put down your chainsaws...

00:12

...because the annual Lumberjack Ball is tonight! Unfortunately, Lumberjack Bill, the one who

00:17

can never get a date...

00:19

...decided to steal the lumberjack dancin' square the night before...

00:22

...leaving the poor lumberjacks to rebuild the whole thing before tonight's ball.

00:26

Here's what the square looked like last night.

00:34

The lumberjack waltz requires there to be a distance of 4 between point B and point

00:39

D.

00:40

Knowing length B prime D prime is 4, what is the length of a side of the square ABCD?

00:47

Here are your choices: Well, to start, it helps to know that squares

00:53

have four right angles and four equal sides.

00:59

Since angle D is in the corner of square ABCD, we know it's a 90 degree angle.

01:05

Zoom in on triangle B prime D D prime. We know it's a right triangle, so we can use

01:12

the Pythagorean theorem to solve it.

01:14

We know its hypotenuse, but not its two side lengths.

01:18

Whatever will the lumberjacks do?

01:20

Since A prime B prime C prime D prime is also a square, we know that angle D prime is also

01:27

90 degrees.

01:29

Angle D D prime C is a straight angle, so it has a measure of 180 degrees.

01:34

Subtract 90 degrees for angle B prime D prime C prime, and we only have 90 degrees to share

01:41

among the two smaller side angles.

01:43

Splitting them up evenly, each angle gets 45 degrees.

01:47

If we do that with all the angles, we'll see that our triangle B prime D D prime is a special

01:52

right triangle, a 45-45-90 triangle.

01:57

Since both its acute angles are congruent, we know the lengths of its legs are congruent.

02:03

Good thing, too; otherwise square dancing would be a big mistake.

02:07

Now we can use the Pythagorean theorem and replace both a and b with the same length:

02:14

x.

02:16

That's the wonderful thing about 45-45-90 triangles. If the length of the leg is x,

02:28

the hypotenuse will always be equal to x times the square root of 2.

02:34

We're looking for the side of the big square, ABCD.

02:38

If we look at the picture, we know that D prime D is the same length as D prime C, so

02:43

we just have to multiply 2 root 2 by 2. That gives us 4 root 2.

02:50

So, long story short... if it isn't already too late... our answer is D.

02:57

Now those lumberjacks can rebuild their perfect square and get ready to dance.

03:01

Swing your chainsaw 'round and 'round!

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