Encuentra todos los ángulos de un triángulo en 3D

Posted on by Rudeus Greyrat

Dadas las coordenadas de 3 vértices de un triángulo en 3D, es decir, A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3). La tarea es encontrar todos los ángulos del triángulo formado por las coordenadas anteriores.
Ejemplos: 
 

Input: 
x1 = -1, y1 = 3, z1 = 2
x2 = 2, y2 = 3, z2 = 5
x3 = 3, y3 = 5, z3 = -2

Output:
angle A =  90.0 degree
angle B =  54.736 degree
angle C =  35.264 degree

Método: 
para encontrar el ángulo A, averigüe las relaciones de dirección de AB y AC: 
las relaciones de dirección de AB = x2-x1, y2-y1, z2-z1 
las relaciones de dirección de AC = x3-x1, y3-y1, z3-z1 
luego el ángulo A =  cos^{-1}\left(\frac{(x_{2}-x_{1})*(x_{3}-x_{1})+(y_{2}-y_{1})*(y_{3}-y_{1})+(z_{2}-z_{1})*(z_{3}-z_{1})}{(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}})*(\sqrt{(x_{3}-x_{1})^{2}+(y_{3}-y_{1})^{2}+(z_{3}-z_{1})^{2}})}\right)
Para encontrar el ángulo B, encuentre las relaciones de dirección de BA y BC: 
relaciones de dirección de BA = x1-x2, y1-y2, z1-z2 
relaciones de dirección de BC = x3-x2, y3-y2, z3-z2 
luego ángulo B =  cos^{-1}\left(\frac{(x_{1}-x_{2})*(x_{3}-x_{2})+(y_{1}-y_{2})*(y_{3}-y_{2})+(z_{1}-z_{2})*(z_{3}-z_{2})}{(\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}+(z_{1}-z_{2})^{2}})*(\sqrt{(x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2}+(z_{3}-z_{2})^{2}})}\right)
Para encontrar el ángulo C, averigüe las relaciones de dirección de CB y CA: 
relaciones de dirección de CB = x2-x3, y2-y3, z2-z3 
relaciones de dirección de CA = x1-x3, y1-y3, z1-z3 
luego ángulo C =  cos^{-1}\left(\frac{(x_{2}-x_{3})*(x_{1}-x_{3})+(y_{2}-y_{3})*(y_{1}-y_{3})+(z_{2}-z_{3})*(z_{1}-z_{3})}{(\sqrt{(x_{2}-x_{3})^{2}+(y_{2}-y_{3})^{2}+(z_{2}-z_{3})^{2}})*(\sqrt{(x_{1}-x_{3})^{2}+(y_{1}-y_{3})^{2}+(z_{1}-z_{3})^{2}})}\right)
Abajo es la implementación del enfoque anterior:
 

C++

//CPP program for finding all angles of a triangle
#include<bits/stdc++.h>
#include<cmath>
using namespace std;
 
// function for finding the angle
float angle_triangle(int x1, int x2, int x3,
            int y1, int y2, int y3, int z1, int z2, int z3)
{
 
    int num = (x2-x1)*(x3-x1)+(y2-y1)*(y3-y1)+(z2-z1)*(z3-z1) ;
 
    float den = sqrt(pow((x2-x1),2)+pow((y2-y1),2)+pow((z2-z1),2))*\
                sqrt(pow((x3-x1),2)+pow((y3-y1),2)+pow((z3-z1),2)) ;
 
    float angle = acos(num / den)*(180.0/3.141592653589793238463) ;
 
    return angle ;
}
 
// Driver code
int main()
{
int x1 = -1;
int y1 = 3;
int z1 = 2;
int x2 = 2;
int y2 = 3;
int z2 = 5;
int x3 = 3;
int y3 = 5;
int z3 = -2;
float angle_A = angle_triangle(x1, x2, x3, y1, y2,
                                y3, z1, z2, z3);
float angle_B = angle_triangle(x2, x3, x1, y2, y3,
                                y1, z2, z3, z1);
float angle_C = angle_triangle(x3, x2, x1, y3,
                            y2, y1, z3, z2, z1);
cout<<"Angles are :"<<endl;
cout<<setprecision(3);
cout<<"angle A = "<<angle_A<<" degree"<<endl;
cout<<"angle B = "<<angle_B<<" degree"<<endl;
cout<<"angle C = "<<angle_C<< " degree"<<endl;
}

Java

//Java program for finding all angles of a triangle
 
class GFG{
// function for finding the angle
static double angle_triangle(int x1, int x2, int x3,
            int y1, int y2, int y3, int z1, int z2, int z3)
{
 
    int num = (x2-x1)*(x3-x1)+(y2-y1)*(y3-y1)+(z2-z1)*(z3-z1) ;
 
    double den = Math.sqrt(Math.pow((x2-x1),2)+
                Math.pow((y2-y1),2)+Math.pow((z2-z1),2))*
                Math.sqrt(Math.pow((x3-x1),2)+
                Math.pow((y3-y1),2)+Math.pow((z3-z1),2)) ;
 
    double angle = Math.acos(num / den)*(180.0/3.141592653589793238463) ;
 
    return angle ;
}
 
// Driver code
public static void main(String[] args)
{
int x1 = -1;
int y1 = 3;
int z1 = 2;
int x2 = 2;
int y2 = 3;
int z2 = 5;
int x3 = 3;
int y3 = 5;
int z3 = -2;
double angle_A = angle_triangle(x1, x2, x3, y1,
                            y2, y3, z1, z2, z3);
double angle_B = angle_triangle(x2, x3, x1,
                            y2, y3, y1, z2, z3, z1);
double angle_C = angle_triangle(x3, x2, x1,
                            y3, y2, y1, z3, z2, z1);
System.out.println("Angles are :");
System.out.println("angle A = "+angle_A+" degree");
System.out.println("angle B = "+angle_B+" degree");
System.out.println("angle C = "+angle_C+" degree");
}
}
// This code is contributed by mits

Python3

# Python Code for finding all angles of a triangle
import math
 
# function for finding the angle
def angle_triangle(x1, x2, x3, y1, y2, y3, z1, z2, z3):
 
    num = (x2-x1)*(x3-x1)+(y2-y1)*(y3-y1)+(z2-z1)*(z3-z1)
 
    den = math.sqrt((x2-x1)**2+(y2-y1)**2+(z2-z1)**2)*\
                math.sqrt((x3-x1)**2+(y3-y1)**2+(z3-z1)**2)
 
    angle = math.degrees(math.acos(num / den))
 
    return round(angle, 3)
 
# driver code    
x1 = -1
y1 = 3
z1 = 2
x2 = 2
y2 = 3
z2 = 5
x3 = 3
y3 = 5
z3 = -2
angle_A = angle_triangle(x1, x2, x3, y1, y2, y3, z1, z2, z3)
angle_B = angle_triangle(x2, x3, x1, y2, y3, y1, z2, z3, z1)
angle_C = angle_triangle(x3, x2, x1, y3, y2, y1, z3, z2, z1)
print("Angles are :")
print("angle A = ", angle_A, "degree")
print("angle B = ", angle_B, "degree")
print("angle C = ", angle_C, "degree")

C#

// C# program for finding all
// angles of a triangle
using System;
                     
class GFG
{
     
// function for finding the angle
static double angle_triangle(int x1, int x2, int x3,
                             int y1, int y2, int y3,
                             int z1, int z2, int z3)
{
 
    int num = (x2 - x1) * (x3 - x1) +
              (y2 - y1) * (y3 - y1) +
              (z2 - z1) * (z3 - z1);
 
    double den = Math.Sqrt(Math.Pow((x2 - x1), 2) +
                           Math.Pow((y2 - y1), 2) +
                           Math.Pow((z2 - z1), 2)) *
                 Math.Sqrt(Math.Pow((x3 - x1), 2) +
                           Math.Pow((y3 - y1), 2) +
                           Math.Pow((z3 - z1), 2));
 
    double angle = Math.Acos(num / den) *
                   (180.0/3.141592653589793238463);
 
    return angle ;
}
 
// Driver code
public static void Main()
{
    int x1 = -1, y1 = 3, z1 = 2;
    int x2 = 2, y2 = 3, z2 = 5;
    int x3 = 3, y3 = 5, z3 = -2;
    double angle_A = angle_triangle(x1, x2, x3,
                                    y1, y2, y3,
                                    z1, z2, z3);
    double angle_B = angle_triangle(x2, x3, x1,
                                    y2, y3, y1,
                                    z2, z3, z1);
    double angle_C = angle_triangle(x3, x2, x1,
                                    y3, y2, y1,
                                    z3, z2, z1);
    Console.WriteLine("Angles are :");
    Console.WriteLine("angle A = " + angle_A +
                                   " degree");
    Console.WriteLine("angle B = " + angle_B +
                                   " degree");
    Console.WriteLine("angle C = " + angle_C +
                                   " degree");
}
}
 
// This code is contributed by 29AjayKumar

PHP

<?php
// PHP program for finding all
// angles of a triangle
 
// function for finding the angle
function angle_triangle($x1, $x2, $x3,
                        $y1, $y2, $y3,
                        $z1, $z2, $z3)
{
 
    $num = ($x2 - $x1) * ($x3 - $x1) +
           ($y2 - $y1) * ($y3 - $y1) +
           ($z2 - $z1) * ($z3 - $z1);
 
    $den = sqrt(pow(($x2 - $x1), 2) +
                pow(($y2 - $y1), 2) +
                pow(($z2 - $z1), 2)) *
           sqrt(pow(($x3 - $x1), 2) +
                pow(($y3 - $y1), 2) +
                pow(($z3 - $z1), 2));
 
    $angle = acos($num / $den) *
                 (180.0 / 3.141592653589793238463);
 
    return $angle ;
}
 
// Driver code
$x1 = -1; $y1 = 3; $z1 = 2;
$x2 = 2; $y2 = 3; $z2 = 5;
$x3 = 3; $y3 = 5; $z3 = -2;
$angle_A = angle_triangle($x1, $x2, $x3, $y1, $y2,
                          $y3, $z1, $z2, $z3);
$angle_B = angle_triangle($x2, $x3, $x1, $y2, $y3,
                          $y1, $z2, $z3, $z1);
$angle_C = angle_triangle($x3, $x2, $x1, $y3,
                          $y2, $y1, $z3, $z2, $z1);
echo "Angles are :\n";
echo "angle A = " . round($angle_A, 3) . " degree\n";
echo "angle B = " . round($angle_B, 3) . " degree\n";
echo "angle C = " . round($angle_C, 3) . " degree\n";
 
// This code is contributed by mits
?>

Javascript

<script>
//Javascript program for finding all angles of a triangle
 
// function for finding the angle
function angle_triangle(x1,x2,x3,y1,y2,y3,z1,z2,z3)
{
    let num = (x2-x1)*(x3-x1)+(y2-y1)*(y3-y1)+(z2-z1)*(z3-z1) ;
   
    let den = Math.sqrt(Math.pow((x2-x1),2)+
                Math.pow((y2-y1),2)+Math.pow((z2-z1),2))*
                Math.sqrt(Math.pow((x3-x1),2)+
                Math.pow((y3-y1),2)+Math.pow((z3-z1),2)) ;
   
    let angle = Math.acos(num / den)*(180.0/3.141592653589793238463) ;
   
    return angle ;
}
 
// Driver code
let x1 = -1;
let y1 = 3;
let z1 = 2;
let x2 = 2;
let y2 = 3;
let z2 = 5;
let x3 = 3;
let y3 = 5;
let z3 = -2;
let angle_A = angle_triangle(x1, x2, x3, y1,
                            y2, y3, z1, z2, z3);
let angle_B = angle_triangle(x2, x3, x1,
                            y2, y3, y1, z2, z3, z1);
let angle_C = angle_triangle(x3, x2, x1,
                            y3, y2, y1, z3, z2, z1);
document.write("Angles are :<br>");
document.write("angle A = "+angle_A+" degree<br>");
document.write("angle B = "+angle_B.toFixed(3)+" degree<br>");
document.write("angle C = "+angle_C.toFixed(3)+" degree<br>");
 
// This code is contributed by rag2127
</script>
Producción: 

Angles are :
angle A =  90.0 degree
angle B =  54.736 degree
angle C =  35.264 degree

 

Publicación traducida automáticamente

Artículo escrito por AashutoshChauhan y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

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