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

Last update on May 30 2025 11:48:45 (UTC/GMT +8 hours)

Triangle Coordinates Finder

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]]

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to compute the coordinates of a triangle's vertices given its side lengths using Heron’s formula and trigonometry.
• Write a Python program to generate triangle vertex coordinates with one vertex at (0,0) and another along the x-axis.
• Write a Python program to determine the third vertex of a triangle when provided with two vertices and the side lengths.
• Write a Python program to use the cosine rule to calculate the coordinates of the triangle’s third point from given side lengths.

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Python Code Editor :

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