Unlock the Power of Right Triangles with NumPy’s Hypotenuse Function

What is the Hypotenuse?

The hypotenuse is the longest side of a right-angled triangle, opposite the right angle. In order to calculate its length, you need to know the lengths of the other two sides.

The Syntax of Hypotenuse

The hypot() function takes three arguments: x1 and x2, which are the input arrays containing the values of the two sides of the right triangle, and out and where, which are optional arguments.

• x1 and x2: These are the input arrays containing the values of the two sides of the right triangle.
• out: This optional argument specifies the output array where the result will be stored.
• where: This optional argument specifies a condition where the hypotenuse length is calculated.

How Hypotenuse Works

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 the two input arrays.

hypotenuse_length = sqrt(x1**2 + x2**2)

Examples

Example 1: Calculating Hypotenuse Length

Let’s take 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.

import numpy as np

side1 = np.array([4, 5, 6])
side2 = np.array([3, 12, 8])

hypotenuse_lengths = np.hypot(side1, side2)
print(hypotenuse_lengths)

Mathematically, this calculation represents the hypotenuse length for the first pair of elements (4, 3) in side1 and side2. The remaining pairs are calculated in the same way.

Example 2: Using Optional Arguments

In this example, we use the optional out and where arguments to customize the output. By specifying out=result, we store the output of the np.hypot() function in the result array. Additionally, where=(side1 > 4) ensures that the calculation of the hypotenuse lengths is performed only for the elements in side1 that are greater than 4.

import numpy as np

side1 = np.array([4, 5, 6])
side2 = np.array([3, 12, 8])
result = np.empty_like(side1)

np.hypot(side1, side2, out=result, where=(side1 > 4))
print(result)

By leveraging the power of hypot(), you can efficiently calculate hypotenuse lengths and unlock new possibilities in your data analysis and scientific computing endeavors.