The following example demonstrates how the `POW`

and `SQRT`

functions work together to compute the hypotenuse of a right triangle using the Pythagorean theorem.

`POW`

- X^{Y}. In this case, 10 to the power of the previous one. See POW Function .`SQRT`

- computes the square root of the input value. See SQRT Function.

The Pythagorean theorem states that in a right triangle the length of each side (x,y) and of the hypotenuse (z) can be represented as the following:

*z ^{2} = x ^{2} + y ^{2} *

Therefore, the length of z can be expressed as the following:

*z = sqrt(x ^{2} + y ^{2} )*

* *For more information on the Pythagorean theorem, see https://en.wikipedia.org/wiki/Pythagorean_theorem.

**Source:**

The dataset below contains values for x and y:

X | Y |
---|---|

3 | 4 |

4 | 9 |

8 | 10 |

30 | 40 |

**Transform:**

You can use the following transform to generate values for z^{2}.

**NOTE: **Do not add this step to your recipe right now.

derive type:single value:(POW(x,2) + POW(y,2)) as:'Z'

You can see how column Z is generated as the sum of squares of the other two columns. Now, wrap the value computation in a`SQRT`

function:
derive type:single value:SQRT((POW(x,2) + POW(y,2))) as: 'Z'

**Results:**

X | Y | Z |
---|---|---|

3 | 4 | 5 |

4 | 9 | 9.848857801796104 |

8 | 10 | 12.806248474865697 |

30 | 40 | 50 |

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