3, 4, 5 Triangle

Need a Right Angle (90°) Fast ... ?

Make a 3,4,5 Triangle !

Connect three lines:

  • 3 long
  • 4 long
  • 5 long

And you will have a right angle (90°)

3,4,5 Triangle

Other Lengths

You can use other lengths by multiplying each side by 2. Or by 10. Or any multiple.

Multiples of 3,4,5

Drawing It

Let us say you need to mark a right angle coming from a point on a wall.

You decide to use 300, 400 and 500 cm lines.

A B C D E
Draw a 300 line along the wall Draw an arc 400 away from the start of the 300 line Draw an arc 500 away from the end of the 300 line Connect from the start of the 300 line to where the arcs cross And you have your "3,4,5" triangle with its right angle

The Mathematics Behind It

The Pythagoras Theorem says:

The square of a (a²) plus the square of b (b²) is equal to the square of c (c²):

a2 + b2 = c2

pythagoras theorem
Let's check if it does work:

32 + 42 = 52

Calculating this becomes:

9 + 16 = 25

Yes, it works !

Other Combinations

Yes, there are other combinations that work (not just by multiplying). Here are two others:

pythagorean triple pythagorean triple
5,12,13 triangle 9,40,41 Triangle
52 + 122 = 132 92 + 402 = 412

But there are infinitely many more.... read Pythagorean Triples for more information.

 

 
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