CodeCogs

Pythagoras Generalized Theorem implementation

Interface

#include <codecogs/maths/geometry/pythgen.h>

using namespace Maths::Geometry;

double pythgen_SetAngleDegRad(const double alpha)
double pythgen_PythagorasGen(const double x, const double y, const double alpha)

Overview

The aim of this module is to implement Pythagoras Generalized Theorem. Given any triangle knowing the value of two sides and the angle between them, one can find out the value of the third side.

According to Pythagora's Generalized Theorem the value of AC side is:

$\textit{AC} = \sqrt{\textit{AB}^2 + \textit{BC}^2 - 2 \cdot \textit{AB} \cdot \textit{BC} \cdot \cos(\widehat{\textit{ABC}}) }$

(1)

This can easily be proven using normal Pythagoras Theorem in the ADC triangle:

$\textit{AC}^2 = \texit{AD}^2 + \textit{DC}^2$

(2)

However,

$\sin{\beta} = \frac{\textit{AD}}{\texit{AB}}$

(3)

and

$\cos{\beta} = \frac{\textit{BD}}{\texit{AB}}$

(4)

Thus, using the last three equations:

$\texit{AC}^2 = \sin^2{\beta} \cdot \texit{AB}^2 + \cos^2{\beta} \cdot \textit{AB} + (\texit{BC} - \texit{BD})^2$

(5)

which is

$\texit{AC}^2 = \texit{AB}^2 +\texit{BC}^2 - 2 \cdot \texit{AB} \cdot \texit{BC} \cdot \cos{\beta}$

(6)

Example 1

#include <stdio.h>
#include <codecogs/maths/geometry/pythgen.h>

int main()
{
    //an equal-sided triangle with the side value of 3.5 
    double thirdSide = pythgen_PythagorasGen(3.5,3.5,60);

    printf("\nThe value of the 3rd side: %.2lf", thirdSide);

    return 0;
}

Output

The value of the 3rd side: 3.50

FUNCTION

pythgen_SetAngleDegRad

Parameters

alpha

value of angle measured in degrees

Returns

value of angle measured in radians

Author

Victor Larie (May 2010)

Interactive Calculator

alpha

Result –

FUNCTION

pythgen_PythagorasGen

Parameters

the value of one side of the triangle

the value of another side of the triangle

alpha

the value of the angle between the sides given in degrees

Returns

the value of the third side of the triangle

Author

Victor Larie (May 2010)

Interactive Calculator

alpha

Result –