# Python NumPy hypot()

The `hypot()` function calculates the hypotenuse length given two arrays that represent the perpendicular sides of a right-angled triangle. Hypotenuse is the longest side of a right-angled triangle, opposite the right angle.

### Example

``````import numpy as np

# create two arrays representing the perpendicular sides of right triangles
x1 = np.array([3, 4, 5])
x2 = np.array([4, 12, 13])

# calculate the hypotenuse using numpy.hypot()
result = np.hypot(x1, x2)

print(result)

# Output : [ 5.  13.  13.]``````

## hypot() Syntax

The syntax of `hypot()` is:

``numpy.round(x1, x2, out = None, where = True)``

## hypot() Arguments

The `hypot()` function takes one argument:

• `x1` - the first input array containing the values of one side of the right triangle
• `x2` - the second input array containing the values of the other side of the right triangle
• `out` (optional) - the output array where the result will be stored
• `where` (optional) - specifies a condition where the hypotenuse length is calculated

## hypot() Return Value

The `hypot()` function returns a new array that contains the element-wise square root of the sum of the squares of the corresponding elements from two input arrays.

## Example 1: Calculate Hypotenuse Length

``````import numpy as np

# create two 1D arrays representing the perpendicular sides of right triangles
side1 = np.array([4, 5, 8])
side2 = np.array([3, 12, 15])

# calculate the hypotenuse lengths using numpy.hypot()
hypotenuse_lengths = np.hypot(side1, side2)

print("Hypotenuse lengths:")
print(hypotenuse_lengths)``````

Output

```Hypotenuse lengths:
[ 5.  13.  17.]```

In this example, we have two 1D arrays side1 and side2 representing the perpendicular sides of right triangles.

The `np.hypot()` function calculates the hypotenuse length for each corresponding pair of elements from side1 and side2.

Mathematically,

``numpy.hypot(4, 3) = sqrt((4^2) + (3^2)) = sqrt(16 + 9) = sqrt(25) = 5``

This calculation represents the hypotenuse length for the first pair of elements (4, 3) in side1 and side2.

All the remaining pairs are calculated in the same way.

## Example 2: Use of Optional out and where Argument in hypot()

``````import numpy as np

# create two arrays representing the perpendicular sides of right triangles
side1 = np.array([4, 5, 8])
side2 = np.array([3, 12, 15])

# create an empty array to store the hypotenuse lengths
result = np.zeros_like(side1, dtype=float)

# calculate the hypotenuse lengths using numpy.hypot() and
# store the results in the 'result' array
np.hypot(side1, side2, out=result, where=(side1 > 4))

print("Hypotenuse lengths:")
print(result)``````

Output

```Hypotenuse lengths:
[ 0. 13. 17.]```

Here,

• `out=result` specifies that the output of the `np.hypot()` function should be stored in the result array.
• `where=(side1 > 4)` specifies that the calculation of the hypotenuse lengths will be performed only for the elements in side1 that are greater than 4.