# Python: Find the coordinates of a triangle with the given side lengths

## Python Programming Puzzles: Exercise-31 with Solution

Write a Python program to find the coordinates of a triangle with given side lengths.

Input: [3, 4, 5] Output: [[0.0, 0.0], [3, 0.0], [3.0, 4.0]] Input: [5, 6, 7] Output: [[0.0, 0.0], [5, 0.0], [3.8, 5.878775382679628]]

**Visual Presentation:**

**Sample Solution:**

**Python Code:**

```
# License: https://bit.ly/3oLErEI
# Define a function named 'test' that takes a list 'sides' representing the side lengths of a triangle
def test(sides):
# Sort the side lengths in ascending order and assign them to variables a, b, and c
a, b, c = sorted(sides)
# Calculate the semi-perimeter of the triangle
s = sum(sides) / 2
# Use Heron's formula to calculate the area of the triangle
area = (s * (s - a) * (s - b) * (s - c)) ** 0.5
# Calculate the height of the triangle
y = 2 * area / a
# Calculate the x-coordinate of the third vertex using the Pythagorean theorem
x = (c ** 2 - y ** 2) ** 0.5
# Return the coordinates of the vertices of the triangle as a list of lists
return [[0.0, 0.0], [a, 0.0], [x, y]]
# Assign a specific list of side lengths 'sides' to the variable
sides = [3, 4, 5]
# Print the side lengths of the triangle
print("Sides of the triangle:", sides)
# Print a message indicating the operation to be performed
print("Coordinates of a triangle with the said side lengths:")
# Print the result of the test function applied to the 'sides' list
print(test(sides))
# Assign another specific list of side lengths 'sides' to the variable
sides = [5, 6, 7]
# Print the side lengths of the triangle
print("\nSides of the triangle:", sides)
# Print a message indicating the operation to be performed
print("Coordinates of a triangle with the said side lengths:")
# Print the result of the test function applied to the 'sides' list
print(test(sides))
```

Sample Output:

Sides of the triangle: [3, 4, 5] Coordinates of a triangle with the said side lengths: [[0.0, 0.0], [3, 0.0], [3.0, 4.0]] Sides of the triangle: [5, 6, 7] Coordinates of a triangle with the said side lengths: [[0.0, 0.0], [5, 0.0], [3.8, 5.878775382679628]]

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