Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 10.05498756211   b = 7.21111025509   c = 14.86660687473

Area: T = 32
Perimeter: p = 32.12770469194
Semiperimeter: s = 16.06435234597

Angle ∠ A = α = 36.6566108416° = 36°39'22″ = 0.64397697828 rad
Angle ∠ B = β = 25.36444171956° = 25°21'52″ = 0.44326925929 rad
Angle ∠ C = γ = 117.9799474388° = 117°58'46″ = 2.05991302779 rad

Height: ha = 6.36882380173
Height: hb = 8.87552031396
Height: hc = 4.30551058816

Median: ma = 10.54875115549
Median: mb = 12.16655250606
Median: mc = 4.61097722286

Inradius: r = 1.99220909681
Circumradius: R = 8.41768294255

Vertex coordinates: A[-3; 6] B[2; -8] C[3; 2]
Centroid: CG[0.66766666667; 0]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[4.20220668858; 1.99220909681]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.3443891584° = 143°20'38″ = 0.64397697828 rad
∠ B' = β' = 154.6365582804° = 154°38'8″ = 0.44326925929 rad
∠ C' = γ' = 62.02105256115° = 62°1'14″ = 2.05991302779 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 + (-8-2)**2 } ; ; a = sqrt{ 101 } = 10.05 ; ;

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{ (-3-3)**2 + (6-2)**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{ (-3-2)**2 + (6-(-8))**2 } ; ; c = sqrt{ 221 } = 14.87 ; ;


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 = 10.05 ; ; b = 7.21 ; ; c = 14.87 ; ;

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

p = a+b+c = 10.05+7.21+14.87 = 32.13 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.13 }{ 2 } = 16.06 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.06 * (16.06-10.05)(16.06-7.21)(16.06-14.87) } ; ; T = sqrt{ 1024 } = 32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32 }{ 10.05 } = 6.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32 }{ 7.21 } = 8.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32 }{ 14.87 } = 4.31 ; ;

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{ 10.05**2-7.21**2-14.87**2 }{ 2 * 7.21 * 14.87 } ) = 36° 39'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.21**2-10.05**2-14.87**2 }{ 2 * 10.05 * 14.87 } ) = 25° 21'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.87**2-10.05**2-7.21**2 }{ 2 * 7.21 * 10.05 } ) = 117° 58'46" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32 }{ 16.06 } = 1.99 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.05 }{ 2 * sin 36° 39'22" } = 8.42 ; ;




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