This article provides an in-depth look into the **hypot** function, accompanied by practical examples. The **hypot** function in PySpark computes the hypotenuse of a right-angle triangle given the two sides. Specifically, for inputs **a** and **b**, it returns the square root of **(a^2 + b^2).**

**Calculate the hypotenuse for given sides:**

```
from pyspark.sql import SparkSession
from pyspark.sql.functions import hypot
spark = SparkSession.builder \
.appName("PySpark hypot Function") \
.getOrCreate()
data = [(3, 4), (5, 12), (8, 15)]
df = spark.createDataFrame(data, ["a", "b"])
df.withColumn("hypotenuse", hypot(df["a"], df["b"])).show()
```

Output:

```
+---+---+----------+
| a| b|hypotenuse|
+---+---+----------+
| 3| 4| 5.0|
| 5| 12| 13.0|
| 8| 15| 17.0|
+---+---+----------+
```

**Use case: Distance calculation**

Imagine a scenario where you have a grid, and you need to compute the distance from the origin (0,0) to various points on this grid. The hypot function can easily compute these distances:

```
grid_data = [(2, 7), (10, 5), (6, 8)]
df_grid = spark.createDataFrame(grid_data, ["x", "y"])
# Calculating distance from origin
df_grid.withColumn("distance_from_origin", hypot(df_grid["x"], df_grid["y"])).show()
```

```
+---+---+--------------------+
| x| y|distance_from_origin|
+---+---+--------------------+
| 2| 7| 7.280109889280518|
| 10| 5| 11.180339887498949|
| 6| 8| 10.0|
+---+---+--------------------+
```

#### When to use hypot?

**Geometry and trigonometry:** Any application that deals with right-angle triangles or needs distance calculations can benefit from `hypot`

.

**Physics simulations:** For scenarios involving vectors, force calculations, or other physics simulations, the `hypot`

function can be useful.

**Data visualizations:** When plotting data or visualizing clusters, `hypot`

can assist in distance calculations, which might be crucial for certain algorithms or representations.

**Spark important urls to refer**