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### Course: High school geometry>Unit 5

Lesson 3: Special right triangles

# Special right triangles proof (part 2)

Showing the ratios of the sides of a 45-45-90 triangle are 1:1:sqrt(2). Created by Sal Khan.

## Want to join the conversation?

• Can you end up with anything other than a isosceles triangle if you have one 45 degree angle and one 90 degree angle?
• Nope, because a triangle ALWAYS has 180˚. No more, no less. If two angles are 45 and 90, then the other HAS to be 45 to make it add to 180. Hope this helps!
• does anyone know where hypotenuse came from?
• The word hypotenuse means essentially "length under", and derives from Latin hypotēnūsa (according to Wikipedia: http://en.wikipedia.org/wiki/Hypotenuse)
• I understand how the 45-45-90 triangle works, but does anyone know a 45-45-90 triangle with whole numbers?
(i need three whole numbers, kind of like the 3-4-5 triangle, but i need it in a 45-45-90 triangle)
Thanks!
• Since a 45-45-90 multiplies by √2 to get from hypotenuse to side, there is no integer representation.
• If the two legs are x and the hypotenuse is three square root 2 how do I find x?
• Well, it depends on what information you have and what you are trying to find
• how do you do pythagorean theorem please
• It was theorem proposed by Pythagoras, which deals with Right angled Triangles only
Pythagorean Theorem just states that in any Right Triangle(With a 90 degree angle) the Length of Hypotenuse squared (Side opposite to 90 degree) is equal to the Sum of the length of squares of its base and adjacent side.
``Commonly known as A^2 + B^2 = C^2``

To be clear, the Side CB in Triangle ABC is equal to the root of Sum of the other two sides, that is √( AB+AC)
`` C                     Angle CAB is a 90 degree angle  •                      Which Makes CB Hypotenuse   •    •                 By Pythagorean Theorem CB^2 = AB^2 + AC^2  •       •              CB =   √AB^2 + BC^2  •           •          Try doing a problem, its on KA, and is Fun!  •               •          •                   •  •                       • A•--------------------------• B``

An Example
Let a Triangle have Legs(Base & Adjacent) of 12 and 5cm. So, the The Third side or Hypotenuse is 12^2 + 5^2 = > 144+25 = √169 = 13cm

``For a reference see Sal's beautiful playlist on Pythagorean Theorem :- https://www.khanacademy.org/math/geometry/right_triangles_topic/pyth_theor/v/pythagorean-theorem``
• In a 45-45-90 triangle, how would you solve for the other two lengths if the base is 8*square root 2? Or please give me an example, thank-you.

I couldn't watch the video because of computer difficulties, my apologies if I'm a little off topic.
• Did you mean the hypotenuse was 8*sqrt(2) units long?

If you know the hypotenuse's length of a 45-45-90 triangle, divide the hypotenuse's length by sqrt(2) to find the length of both of the legs. In this case, the legs have a length of 8 units.

Did you mean one of the legs was 8*sqrt(2) units long?
If you know the length of one of the legs of a 45-45-90 triangle, the other leg has the same length. For this triangle, the other leg has a length of 8*sqrt(2) units. The hypotenuse's length can be found by multiplying the leg's length by sqrt(2). Tis triangle's hypotenuse has a length of 16 units.

In a 45-45-90 triangle, both of the legs have the same length and the ratio of one leg to the hypotenuse is 1:sqrt(2). I hope this helps!
• This may sound like a stupid question but what video precedes this one? Sal says in the previous video... but i cant find it.
• Where did the name right angle come from?
• The meaning of 'right' in right angle possibly refers to the Latin adjective rectus erect, straight, upright, perpendicular'.
In this case the origin of the term could come from architecture where right angles would be used in building structures. In this scenario right would refer to the correct way of doing something such as laying beams for a house.
(1 vote)
• sal, how do write so neat with a mousepad? when i write, it is terrible.