Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 3.16222776602   b = 11.18803398875   c = 8.06222577483

Area: T = 2.5
Perimeter: p = 22.4054875296
Semiperimeter: s = 11.2022437648

Angle ∠ A = α = 3.18798301199° = 3°10'47″ = 0.05554985052 rad
Angle ∠ B = β = 168.6990067526° = 168°41'24″ = 2.94441970937 rad
Angle ∠ C = γ = 8.13301023542° = 8°7'48″ = 0.14218970546 rad

Height: ha = 1.58111388301
Height: hb = 0.44772135955
Height: hc = 0.62201736729

Median: ma = 9.61876920308
Median: mb = 2.5
Median: mc = 7.15989105316

Inradius: r = 0.22331657143
Circumradius: R = 28.50443856275

Vertex coordinates: A[8; 2] B[4; -5] C[3; -8]
Centroid: CG[5; -3.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-1.11658285717; 0.22331657143]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.822016988° = 176°49'13″ = 0.05554985052 rad
∠ B' = β' = 11.3109932474° = 11°18'36″ = 2.94441970937 rad
∠ C' = γ' = 171.8769897646° = 171°52'12″ = 0.14218970546 rad

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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{ (4-3)**2 + (-5-(-8))**2 } ; ; a = sqrt{ 10 } = 3.16 ; ;

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{ (8-3)**2 + (2-(-8))**2 } ; ; b = sqrt{ 125 } = 11.18 ; ;

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{ (8-4)**2 + (2-(-5))**2 } ; ; c = sqrt{ 65 } = 8.06 ; ;


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 = 3.16 ; ; b = 11.18 ; ; c = 8.06 ; ;

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

p = a+b+c = 3.16+11.18+8.06 = 22.4 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.4 }{ 2 } = 11.2 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.2 * (11.2-3.16)(11.2-11.18)(11.2-8.06) } ; ; T = sqrt{ 6.25 } = 2.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.5 }{ 3.16 } = 1.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.5 }{ 11.18 } = 0.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.5 }{ 8.06 } = 0.62 ; ;

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{ 3.16**2-11.18**2-8.06**2 }{ 2 * 11.18 * 8.06 } ) = 3° 10'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11.18**2-3.16**2-8.06**2 }{ 2 * 3.16 * 8.06 } ) = 168° 41'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.06**2-3.16**2-11.18**2 }{ 2 * 11.18 * 3.16 } ) = 8° 7'48" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.5 }{ 11.2 } = 0.22 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.16 }{ 2 * sin 3° 10'47" } = 28.5 ; ;




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