3, 4, 5 Triangle
Need a Right Angle (90°) ?
Make a 3,4,5 Triangle !
Connect three lines:
And you will have a right angle (90°) |
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Other Lengths
You can use other lengths by multipying each side by 2. Or by 10. Or any multiple.
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.
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| 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:
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The square of a (a²) plus the square of b (b²) is equal to the square of c (c²):
a2 + b2 = c2 |
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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:
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| 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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