Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 9.22195444573   b = 4.12331056256   c = 5.09990195136

Area: T = 0.5
Perimeter: p = 18.44216695965
Semiperimeter: s = 9.22108347983

Angle ∠ A = α = 177.2743689006° = 177°16'25″ = 3.09440095503 rad
Angle ∠ B = β = 1.21988752351° = 1°13'8″ = 0.0211273386 rad
Angle ∠ C = γ = 1.50774357588° = 1°30'27″ = 0.02663097173 rad

Height: ha = 0.10884652289
Height: hb = 0.2432535625
Height: hc = 0.19661161351

Median: ma = 0.5
Median: mb = 7.15989105316
Median: mc = 6.67108320321

Inradius: r = 0.05442250253
Circumradius: R = 96.91549111334

Vertex coordinates: A[5; -1] B[6; -6] C[4; 3]
Centroid: CG[5; -1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.5498576188; 0.05442250253]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 2.72663109939° = 2°43'35″ = 3.09440095503 rad
∠ B' = β' = 178.7811124765° = 178°46'52″ = 0.0211273386 rad
∠ C' = γ' = 178.4932564241° = 178°29'33″ = 0.02663097173 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{ (6-4)**2 + (-6-3)**2 } ; ; a = sqrt{ 85 } = 9.22 ; ;

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{ (5-4)**2 + (-1-3)**2 } ; ; b = sqrt{ 17 } = 4.12 ; ;

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{ (5-6)**2 + (-1-(-6))**2 } ; ; c = sqrt{ 26 } = 5.1 ; ;


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 = 9.22 ; ; b = 4.12 ; ; c = 5.1 ; ;

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

p = a+b+c = 9.22+4.12+5.1 = 18.44 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.44 }{ 2 } = 9.22 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.22 * (9.22-9.22)(9.22-4.12)(9.22-5.1) } ; ; T = sqrt{ 0.25 } = 0.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.5 }{ 9.22 } = 0.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.5 }{ 4.12 } = 0.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.5 }{ 5.1 } = 0.2 ; ;

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{ 9.22**2-4.12**2-5.1**2 }{ 2 * 4.12 * 5.1 } ) = 177° 16'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.12**2-9.22**2-5.1**2 }{ 2 * 9.22 * 5.1 } ) = 1° 13'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.1**2-9.22**2-4.12**2 }{ 2 * 4.12 * 9.22 } ) = 1° 30'27" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.5 }{ 9.22 } = 0.05 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.22 }{ 2 * sin 177° 16'25" } = 96.91 ; ;




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