Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 1.41442135624   b = 7.21111025509   c = 5.83109518948

Area: T = 1
Perimeter: p = 14.45662680081
Semiperimeter: s = 7.22881340041

Angle ∠ A = α = 2.72663109939° = 2°43'35″ = 0.04875831033 rad
Angle ∠ B = β = 165.9643756532° = 165°57'50″ = 2.89766139905 rad
Angle ∠ C = γ = 11.3109932474° = 11°18'36″ = 0.19773955598 rad

Height: ha = 1.41442135624
Height: hb = 0.27773500981
Height: hc = 0.34329971703

Median: ma = 6.51992024052
Median: mb = 2.23660679775
Median: mc = 4.30111626335

Inradius: r = 0.13883482929
Circumradius: R = 14.86660687473

Vertex coordinates: A[1; 4] B[-2; -1] C[-3; -2]
Centroid: CG[-1.33333333333; 0.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0.55333931714; 0.13883482929]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.2743689006° = 177°16'25″ = 0.04875831033 rad
∠ B' = β' = 14.03662434679° = 14°2'10″ = 2.89766139905 rad
∠ C' = γ' = 168.6990067526° = 168°41'24″ = 0.19773955598 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{ (-2-(-3))**2 + (-1-(-2))**2 } ; ; a = sqrt{ 2 } = 1.41 ; ;

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{ (1-(-3))**2 + (4-(-2))**2 } ; ; b = sqrt{ 52 } = 7.21 ; ;

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{ (1-(-2))**2 + (4-(-1))**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 = 1.41 ; ; b = 7.21 ; ; c = 5.83 ; ;

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

p = a+b+c = 1.41+7.21+5.83 = 14.46 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14.46 }{ 2 } = 7.23 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.23 * (7.23-1.41)(7.23-7.21)(7.23-5.83) } ; ; T = sqrt{ 1 } = 1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1 }{ 1.41 } = 1.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1 }{ 7.21 } = 0.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1 }{ 5.83 } = 0.34 ; ;

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{ 1.41**2-7.21**2-5.83**2 }{ 2 * 7.21 * 5.83 } ) = 2° 43'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.21**2-1.41**2-5.83**2 }{ 2 * 1.41 * 5.83 } ) = 165° 57'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.83**2-1.41**2-7.21**2 }{ 2 * 7.21 * 1.41 } ) = 11° 18'36" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1 }{ 7.23 } = 0.14 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.41 }{ 2 * sin 2° 43'35" } = 14.87 ; ;




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