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°) |
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Other Lengths
You can use other lengths by multiplying 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.