Learn shortcut ratios for the side lengths of two common right triangles: 45°-45°-90° and 30°-60°-90° triangles. The ratios come straight from the Pythagorean theorem.

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Brieanna Oscar

8 years agoPosted 8 years ago. Direct link to Brieanna Oscar's post “im so used to doing a2+b2...”

im so used to doing a2+b2=c 2 what has changed I do not understand

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(31 votes)

Jack Huber

8 years agoPosted 8 years ago. Direct link to Jack Huber's post “With 45-45-90 and 30-60-9...”

With 45-45-90 and 30-60-90 triangles you can figure out all the sides of the triangle by using only one side. If you know one short side of a 45-45-90 triangle the short side is the same length and the hypotenuse is root 2 times larger. If you know the hypotenuse of a 45-45-90 triangle the other sides are root 2 times smaller. If you know the 30-degree side of a 30-60-90 triangle the 60-degree side is root 3 times larger and the hypotenuse is twice as long. if you know the 60-degree side of a 30-60-90 triangle the 30-degree side is root 3 times smaller and the hypotenuse is 2/root 3 times longer. If you know the hypotenuse of a 30-60-90 triangle the 30-degree is half as long and the 60-degree side is root 3/2 times as long.

(130 votes)

Aryan

7 years agoPosted 7 years ago. Direct link to Aryan's post “What is the difference be...”

What is the difference between congruent triangles and similar triangles?

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(12 votes)

David Severin

7 years agoPosted 7 years ago. Direct link to David Severin's post “Congruent are same size a...”

Congruent are same size and same shape

Similar are same shape but different size

Both have to have one to one correspondence between their angles, but congruent also has one to one correspondence between their sides, but similar sides are equally proportional(44 votes)

- See Also1.2: Special Right Triangles
anthony.lozano

7 years agoPosted 7 years ago. Direct link to anthony.lozano's post “what can i do to not get ...”

what can i do to not get confused with what im doing ?

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(13 votes)

George C

7 years agoPosted 7 years ago. Direct link to George C's post “I'd make sure I knew the ...”

I'd make sure I knew the basic skills for the topic. For special triangles some skills you need to master are: Angles, Square roots, and most importantly

**The Pythagorean Theorem**. Another source you can use is the hints in the exercises, they can help guide you.(28 votes)

april_oh_

3 years agoPosted 3 years ago. Direct link to april_oh_'s post “I use this trick on 30, 6...”

I use this trick on 30, 60, 90 triangles and I've never gotten a single wrong -

1. The small leg to the hypotenuse is times 2, Hypotenuse to the small leg is divided by 2.

2. The small leg (x) to the longer leg is x radical threeFor Example-

Pretend that the short leg is 4 and we will represent that as "x." And we are trying to find the length of the hypotenuse side and the long side. To find the lengths of the hypotenuse from the short leg (x), all we have to do is x times 2, which in this case is 4 times 2. Four times 2 is 8. The length of the hypotenuse side is 8. That is how to find the hypotenuse from the short leg. But are we done yet? No, we are not. We still have to find the length of the long leg. Since the short leg (x) is 4, we have to do "x" radical three. I came to a conclusion that the long leg is 4 radical 3.-This works everytime

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(15 votes)

mud

2 years agoPosted 2 years ago. Direct link to mud's post “wow, thanks :)”

wow, thanks :)

(9 votes)

Esa Abuzar

4 years agoPosted 4 years ago. Direct link to Esa Abuzar's post “if I get 30.1 degrees, is...”

if I get 30.1 degrees, is it still a special triangle

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(7 votes)

David Severin

4 years agoPosted 4 years ago. Direct link to David Severin's post “No, but it is approximate...”

No, but it is approximately a special triangle. I do not know how you can tell the difference on a protractor between 30 and 30.1 degrees.

(18 votes)

sydney

5 years agoPosted 5 years ago. Direct link to sydney's post “How can you tell if a tri...”

How can you tell if a triangle is a 30 60 90 triangle vs a 45 45 90 triangle? Help!

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(6 votes)

hannahmorrell

5 years agoPosted 5 years ago. Direct link to hannahmorrell's post “A 45 45 90 triangle is is...”

A 45 45 90 triangle is isosceles. The two legs are equal. A 30 60 90 triangle has the hypotenuse 2 times as long as the short leg. Hope this helps!

(19 votes)

gracieseitz

5 years agoPosted 5 years ago. Direct link to gracieseitz's post “Let's say that there is a...”

Let's say that there is a 30-60-90 triangle and I need to figure out the side opposite of the 60 degree angle and the hypotenuse is something like 6 times the square root of 3. I know that to get the answer I need to multiply this by the square root of 3 over 2. Do I multiply everything or is there a certain time when I divide or do something with square roots and/or roots? Would the answer to this problem be 36 (square root of 3 times the square root of 3 to get 3, 2 times 6 to get 12, and 12 times 3 to get 36)?

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(6 votes)

Rick

5 years agoPosted 5 years ago. Direct link to Rick's post “The answer to your proble...”

The answer to your problem is actually 9. You are correct about multiplying the square root of 3 / 2 by the hypotenuse (6 * root of 3), but your answer is incorrect. This is because if you multiply the square root of 3 by 6 times the root of three, that would be the same as multiplying 3 by 6 (because the square root of 3 squared is 3). 3 by 6 is 18, and that divided by 2 would equal 9, which is the correct answeer.

(10 votes)

jinseo.park

5 years agoPosted 5 years ago. Direct link to jinseo.park's post “Are special right triangl...”

Are special right triangles still classified as right triangles?

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(3 votes)

Markarino /TEE/DGPE-PI1 #Evaluate

5 years agoPosted 5 years ago. Direct link to Markarino /TEE/DGPE-PI1 #Evaluate's post “Boy, I hope you're still ...”

Boy, I hope you're still around. I hate that nobody has answered this very good question.

The short answer is, yes.

Unfortunately, I'm new around here, but I can tell you what I understand. I don't know if special triangles are an actual thing, or just a category KA came up with to describe this lesson. What I can tell you is that the special triangles that they describe here in these lessons are the 30-60-90 triangle, which is always a right triangle (because of the 90 degree angle) and the 45-45-90 right triangle.

(15 votes)

Siena

5 years agoPosted 5 years ago. Direct link to Siena's post “Can't you just use SOH CA...”

Can't you just use SOH CAH TOA to find al of these?

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(6 votes)

David Severin

5 years agoPosted 5 years ago. Direct link to David Severin's post “Yes, but special right tr...”

Yes, but special right triangles have constant ratios, so if you learn how to do this, you can get answers faster.

(7 votes)

essa.ongchangco223

a year agoPosted a year ago. Direct link to essa.ongchangco223's post “generally, this method is...”

generally, this method is mostly a short way of solving each side making it quicker than using the Pythagorean theorem. Right?

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(7 votes)

Michelle Banks

6 months agoPosted 6 months ago. Direct link to Michelle Banks 's post “In some ways, yes. Still,...”

In some ways, yes. Still, a good checking step if you have whole and real numbers is to plug it into the Pythagorean theorem. just restating

(2 votes)