Triangle calculator VC

Please enter the coordinates of the three vertices


Acute scalene triangle.

Sides: a = 9.89994949366   b = 5.38551648071   c = 9.22195444573

Area: T = 24.5
Perimeter: p = 24.5044204201
Semiperimeter: s = 12.25221021005

Angle ∠ A = α = 80.72773982228° = 80°43'39″ = 1.40989588956 rad
Angle ∠ B = β = 32.47111922908° = 32°28'16″ = 0.56767292175 rad
Angle ∠ C = γ = 66.80114094864° = 66°48'5″ = 1.16659045405 rad

Height: ha = 4.95497474683
Height: hb = 9.09990715707
Height: hc = 5.31547962166

Median: ma = 5.70108771255
Median: mb = 9.17987798753
Median: mc = 6.5

Inradius: r = 21.9996568588
Circumradius: R = 5.01552827662

Vertex coordinates: A[6; 3] B[-3; 5] C[4; -2]
Centroid: CG[2.33333333333; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.1422317921; 21.9996568588]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.27326017772° = 99°16'21″ = 1.40989588956 rad
∠ B' = β' = 147.5298807709° = 147°31'44″ = 0.56767292175 rad
∠ C' = γ' = 113.1998590514° = 113°11'55″ = 1.16659045405 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 ; ; a = sqrt{ ( beta _x- gamma _x)**2 + ( beta _y- gamma _y)**2 } ; ; a = sqrt{ (-3-4)**2 + (5-(-2))**2 } ; ; a = sqrt{ 98 } = 9.9 ; ;

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 ; ; b = sqrt{ ( alpha _x- gamma _x)**2 + ( alpha _y- gamma _y)**2 } ; ; b = sqrt{ (6-4)**2 + (3-(-2))**2 } ; ; b = sqrt{ 29 } = 5.39 ; ;

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 ; ; c = sqrt{ ( alpha _x- beta _x)**2 + ( alpha _y- beta _y)**2 } ; ; c = sqrt{ (6-(-3))**2 + (3-5)**2 } ; ; c = sqrt{ 85 } = 9.22 ; ;


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 = 9.9 ; ; b = 5.39 ; ; c = 9.22 ; ;

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

p = a+b+c = 9.9+5.39+9.22 = 24.5 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.5 }{ 2 } = 12.25 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.25 * (12.25-9.9)(12.25-5.39)(12.25-9.22) } ; ; T = sqrt{ 600.25 } = 24.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.5 }{ 9.9 } = 4.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.5 }{ 5.39 } = 9.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.5 }{ 9.22 } = 5.31 ; ;

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{ 9.9**2-5.39**2-9.22**2 }{ 2 * 5.39 * 9.22 } ) = 80° 43'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.39**2-9.9**2-9.22**2 }{ 2 * 9.9 * 9.22 } ) = 32° 28'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.22**2-9.9**2-5.39**2 }{ 2 * 5.39 * 9.9 } ) = 66° 48'5" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.5 }{ 12.25 } = 2 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.9 }{ 2 * sin 80° 43'39" } = 5.02 ; ;




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

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