Special right triangles review (article) | Khan Academy (2024)

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

    (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...”

      Special right triangles review (article) | Khan Academy (4)

      Special right triangles review (article) | Khan Academy (5)

      Special right triangles review (article) | Khan Academy (6)

      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?

    (12 votes)

    • David Severin

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

      Special right triangles review (article) | Khan Academy (10)

      Special right triangles review (article) | Khan Academy (11)

      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)

  • 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 ?

    (13 votes)

    • George C

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

      Special right triangles review (article) | Khan Academy (15)

      Special right triangles review (article) | Khan Academy (16)

      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 three

    For 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

    (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

    (7 votes)

    • David Severin

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

      Special right triangles review (article) | Khan Academy (23)

      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!

    (6 votes)

    • hannahmorrell

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

      Special right triangles review (article) | Khan Academy (27)

      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)?

    (6 votes)

    • Rick

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

      Special right triangles review (article) | Khan Academy (31)

      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?

    (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 ...”

      Special right triangles review (article) | Khan Academy (35)

      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?

    (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?

    (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)

Special right triangles review (article) | Khan Academy (2024)

FAQs

What is a 45-45-90 special right triangle Khan Academy? ›

A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long. Created by Sal Khan.

What is a 30-60-90 and 45-45-90 special right triangle? ›

The formula for the 2 types of special right triangles is expressed in the form of the ratio of the sides and can be written as follows: 30° 60° 90° triangle formula: Short leg: Long leg : Hypotenuse = x: x√3: 2x. 45° 45° 90° triangle formula: Leg : Leg: Hypotenuse = x: x: x√2.

How to remember 30-60-90 triangles? ›

In any 30-60-90 triangle, you see the following: The shortest leg is across from the 30-degree angle, the length of the hypotenuse is always double the length of the shortest leg, and you can find the length of the long leg by multiplying the short leg by the square root of 3.

How to solve 45-45-90 triangles? ›

The 45-45-90 triangle theorem is also called the Pythagorean theorem. In accordance with this theorem, legs a and b are the same value. To solve for the hypotenuse, use the equation c = a times the square root of 2. To solve for the legs, use the equation a = c divided by the square root of 2.

What is the 30 60 90 rule? ›

What is the 30 60 90 Triangle rule? The 30-60-90 triangle rule is for finding the the lengths of two sides when one side is given. The shorter side is opposite the 30 degree angle, the longer side is opposite the 60 degree angle, and the hypotenuse is opposite the 90 degree angle.

How to prove 30-60-90 triangle? ›

30-60-90-Triangle Theorem

Statement: The length of the hypotenuse is twice the length of the shortest side and the length of the other side is √3 times the length of the shortest side in a 30-60-90-Triangle.

Why is a 30-60-90 triangle special? ›

A special right triangle with angles 30°, 60°, and 90° is called a 30-60-90 triangle. The angles of a 30-60-90 triangle are in the ratio 1 : 2 : 3. Since 30° is the smallest angle in the triangle, the side opposite to the 30° angle is always the smallest (shortest leg).

How to solve right triangles? ›

Solving right triangles

We can use the Pythagorean theorem and properties of sines, cosines, and tangents to solve the triangle, that is, to find unknown parts in terms of known parts. Pythagorean theorem: a2 + b2 = c2. Sines: sin A = a/c, sin B = b/c. Cosines: cos A = b/c, cos B = a/c.

What is Soh Cah Toa? ›

"SOHCAHTOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent, (1) (2)

What is the angle of depression? ›

The angle of depression is the angle between the horizontal line and the observation of the object from the horizontal line. It is basically used to get the distance of the two objects where the angles and an object's distance from the ground are known to us.

Can a right angle triangle be isosceles? ›

An Isosceles Right Triangle is a right triangle that consists of two equal length legs. Since the two legs of the right triangle are equal in length, the corresponding angles would also be congruent.

Are 345 triangles 30-60-90? ›

No. The sides of a 30–60–90 triangle are in the proportion 1 - √3 - 2, not 3–4–5. Or, looking at it the other way, the angles of a 3–4–5 triangle are about 36.87°, 53.13° and 90°.

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