Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 12.24774487139   b = 5.09990195136   c = 7.48333147735

Area: T = 8.66602540378
Perimeter: p = 24.83297830011
Semiperimeter: s = 12.41548915005

Angle ∠ A = α = 153.0044491599° = 153°16″ = 2.67704321487 rad
Angle ∠ B = β = 10.89333946491° = 10°53'36″ = 0.19901256033 rad
Angle ∠ C = γ = 16.1022113752° = 16°6'8″ = 0.28110349015 rad

Height: ha = 1.41442135624
Height: hb = 3.39768311024
Height: hc = 2.31545502494

Median: ma = 1.87108286934
Median: mb = 9.82334413522
Median: mc = 8.6022325267

Inradius: r = 0.69875698529
Circumradius: R = 13.49107375632

Vertex coordinates: A[3; 1; -2] B[-1; 3; 4] C[4; -2; -6]
Centroid: CG[2; 0.66766666667; -1.33333333333]
Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 26.99655084011° = 26°59'44″ = 2.67704321487 rad
∠ B' = β' = 169.1076605351° = 169°6'24″ = 0.19901256033 rad
∠ C' = γ' = 163.8987886248° = 163°53'52″ = 0.28110349015 rad

Calculate another triangle




How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem

a = | beta gamma | = | beta - gamma | ; ; a**2 = ( beta _x- gamma _x)**2 + ( beta _y- gamma _y)**2 + ( beta _z- gamma _z)**2 ; ; a = sqrt{ ( beta _x- gamma _x)**2 + ( beta _y- gamma _y)**2 + ( beta _z- gamma _z)**2 } ; ; a = sqrt{ (-1-4)**2 + (3-(-2))**2 + (4 - (-6))**2 } ; ; a = sqrt{ 150 } = 12.25 ; ;

2. We compute side b from coordinates using the Pythagorean theorem

b = | alpha gamma | = | alpha - gamma | ; ; b**2 = ( alpha _x- gamma _x)**2 + ( alpha _y- gamma _y)**2 + ( alpha _z- gamma _z)**2 ; ; b = sqrt{ ( alpha _x- gamma _x)**2 + ( alpha _y- gamma _y)**2 + ( alpha _z- gamma _z)**2 } ; ; b = sqrt{ (3-4)**2 + (1-(-2))**2 + (-2 - (-6))**2 } ; ; b = sqrt{ 26 } = 5.1 ; ;

3. We compute side c from coordinates using the Pythagorean theorem

c = | alpha beta | = | alpha - beta | ; ; c**2 = ( alpha _x- beta _x)**2 + ( alpha _y- beta _y)**2 + ( alpha _z- beta _z)**2 ; ; c = sqrt{ ( alpha _x- beta _x)**2 + ( alpha _y- beta _y)**2 + ( alpha _z- beta _z)**2 } ; ; c = sqrt{ (3-(-1))**2 + (1-3)**2 + (-2 - 4)**2 } ; ; c = sqrt{ 56 } = 7.48 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 12.25 ; ; b = 5.1 ; ; c = 7.48 ; ;

4. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 12.25+5.1+7.48 = 24.83 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.83 }{ 2 } = 12.41 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.41 * (12.41-12.25)(12.41-5.1)(12.41-7.48) } ; ; T = sqrt{ 75 } = 8.66 ; ;

7. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.66 }{ 12.25 } = 1.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.66 }{ 5.1 } = 3.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.66 }{ 7.48 } = 2.31 ; ;

8. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 12.25**2-5.1**2-7.48**2 }{ 2 * 5.1 * 7.48 } ) = 153° 16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.1**2-12.25**2-7.48**2 }{ 2 * 12.25 * 7.48 } ) = 10° 53'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.48**2-12.25**2-5.1**2 }{ 2 * 5.1 * 12.25 } ) = 16° 6'8" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.66 }{ 12.41 } = 0.7 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.25 }{ 2 * sin 153° 16" } = 13.49 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.