Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 8.48552813742   b = 3.16222776602   c = 5.83109518948

Area: T = 6
Perimeter: p = 17.47985109293
Semiperimeter: s = 8.73992554646

Angle ∠ A = α = 139.3998705355° = 139°23'55″ = 2.43329663815 rad
Angle ∠ B = β = 14.03662434679° = 14°2'10″ = 0.24549786631 rad
Angle ∠ C = γ = 26.56550511771° = 26°33'54″ = 0.4643647609 rad

Height: ha = 1.41442135624
Height: hb = 3.79547331922
Height: hc = 2.05879830217

Median: ma = 2
Median: mb = 7.10663352018
Median: mc = 5.70108771255

Inradius: r = 0.68765573417
Circumradius: R = 6.51992024052

Vertex coordinates: A[0; 0] B[-3; 5] C[3; -1]
Centroid: CG[0; 1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.74662293667; 0.68765573417]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 40.6011294645° = 40°36'5″ = 2.43329663815 rad
∠ B' = β' = 165.9643756532° = 165°57'50″ = 0.24549786631 rad
∠ C' = γ' = 153.4354948823° = 153°26'6″ = 0.4643647609 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{ (-3-3)**2 + (5-(-1))**2 } ; ; a = sqrt{ 72 } = 8.49 ; ;

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{ (0-3)**2 + (0-(-1))**2 } ; ; b = sqrt{ 10 } = 3.16 ; ;

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{ (0-(-3))**2 + (0-5)**2 } ; ; c = sqrt{ 34 } = 5.83 ; ;


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 = 8.49 ; ; b = 3.16 ; ; c = 5.83 ; ;

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

p = a+b+c = 8.49+3.16+5.83 = 17.48 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.48 }{ 2 } = 8.74 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.74 * (8.74-8.49)(8.74-3.16)(8.74-5.83) } ; ; T = sqrt{ 36 } = 6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6 }{ 8.49 } = 1.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6 }{ 3.16 } = 3.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6 }{ 5.83 } = 2.06 ; ;

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{ 8.49**2-3.16**2-5.83**2 }{ 2 * 3.16 * 5.83 } ) = 139° 23'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.16**2-8.49**2-5.83**2 }{ 2 * 8.49 * 5.83 } ) = 14° 2'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.83**2-8.49**2-3.16**2 }{ 2 * 3.16 * 8.49 } ) = 26° 33'54" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6 }{ 8.74 } = 0.69 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.49 }{ 2 * sin 139° 23'55" } = 6.52 ; ;




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