Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 8.06222577483   b = 12.64991106407   c = 20.61655281281

Area: T = 10
Perimeter: p = 41.32768965171
Semiperimeter: s = 20.66334482585

Angle ∠ A = α = 4.3998705355° = 4°23'55″ = 0.07767718913 rad
Angle ∠ B = β = 6.9111227119° = 6°54'40″ = 0.12106236686 rad
Angle ∠ C = γ = 168.6990067526° = 168°41'24″ = 2.94441970937 rad

Height: ha = 2.48106946918
Height: hb = 1.58111388301
Height: hc = 0.97701425001

Median: ma = 16.62107701386
Median: mb = 14.31878210633
Median: mc = 2.5

Inradius: r = 0.48439463324
Circumradius: R = 52.55994901041

Vertex coordinates: A[-8; 1] B[12; 6] C[4; 5]
Centroid: CG[2.66766666667; 4]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.99325572425; 0.48439463324]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.6011294645° = 175°36'5″ = 0.07767718913 rad
∠ B' = β' = 173.0898772881° = 173°5'20″ = 0.12106236686 rad
∠ C' = γ' = 11.3109932474° = 11°18'36″ = 2.94441970937 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{ (12-4)**2 + (6-5)**2 } ; ; a = sqrt{ 65 } = 8.06 ; ;

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{ (-8-4)**2 + (1-5)**2 } ; ; b = sqrt{ 160 } = 12.65 ; ;

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{ (-8-12)**2 + (1-6)**2 } ; ; c = sqrt{ 425 } = 20.62 ; ;


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 = 8.06 ; ; b = 12.65 ; ; c = 20.62 ; ;

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

p = a+b+c = 8.06+12.65+20.62 = 41.33 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41.33 }{ 2 } = 20.66 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.66 * (20.66-8.06)(20.66-12.65)(20.66-20.62) } ; ; T = sqrt{ 100 } = 10 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10 }{ 8.06 } = 2.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10 }{ 12.65 } = 1.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10 }{ 20.62 } = 0.97 ; ;

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{ 8.06**2-12.65**2-20.62**2 }{ 2 * 12.65 * 20.62 } ) = 4° 23'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 12.65**2-8.06**2-20.62**2 }{ 2 * 8.06 * 20.62 } ) = 6° 54'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20.62**2-8.06**2-12.65**2 }{ 2 * 12.65 * 8.06 } ) = 168° 41'24" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10 }{ 20.66 } = 0.48 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.06 }{ 2 * sin 4° 23'55" } = 52.56 ; ;




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

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