3, 4, 5 Triangle
Need a Right Angle (90°) Fast ... ?
Make a 3,4,5 Triangle !
Connect three lines:
And you will have a right angle (90°)
You can use other lengths by multiplying each side by 2. Or by 10. Or any multiple.
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.
|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:
In a right-angled triangle, the square of a (a2) plus the square of b (b2) is equal to the square of c (c2):
a2 + b2 = c2
Let's check if it does work:
32 + 42 = 52
Calculating this becomes:
9 + 16 = 25
Yes, it works !
Yes, there are other combinations that work (not just by multiplying). Here are two others:
|5,12,13 triangle||9,40,41 Triangle|
|52 + 122 = 132||92 + 402 = 412|
|25 + 144 = 169||(try it yourself)|
And there are infinitely many more.... read Pythagorean Triples for more information.