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pythgen

Pythagoras Generalized Theorem implementation

Controller: lariev

Contents

Interface
Pythgen SetAngleDegRad
Pythgen PythagorasGen
Page Comments

Interface

C++

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.

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

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

(2)

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

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

(3)

However,

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

(4)

and

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

(5)

Thus, using the last three equations:

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

(6)

which is

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

(7)

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

Pythgen SetAngleDegRad

doublepythgen_SetAngleDegRad( const double alpha )

Parameters

alpha

value of angle measured in degrees

Returns

value of angle measured in radians

Authors

Victor Larie (May 2010)

Source Code

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Pythgen PythagorasGen

doublepythgen_PythagorasGen(	const double	`x`
	const double	`y`
	const double	`alpha`	)