Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 5.38551648071   b = 9.84988578018   c = 4.4722135955

Area: T = 1
Perimeter: p = 19.70661585639
Semiperimeter: s = 9.8533079282

Angle ∠ A = α = 2.60325622025° = 2°36'9″ = 0.04554232794 rad
Angle ∠ B = β = 175.2366358309° = 175°14'11″ = 3.05884514217 rad
Angle ∠ C = γ = 2.16110794882° = 2°9'40″ = 0.03877179525 rad

Height: ha = 0.37113906764
Height: hb = 0.2033069233
Height: hc = 0.44772135955

Median: ma = 7.15989105316
Median: mb = 0.5
Median: mc = 7.61657731059

Inradius: r = 0.10114911147
Circumradius: R = 59.29879763567

Vertex coordinates: A[0; -3] B[-2; 1] C[-4; 6]
Centroid: CG[-2; 1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-1.21878933769; 0.10114911147]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.3977437798° = 177°23'51″ = 0.04554232794 rad
∠ B' = β' = 4.76436416907° = 4°45'49″ = 3.05884514217 rad
∠ C' = γ' = 177.8398920512° = 177°50'20″ = 0.03877179525 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{ (-2-(-4))**2 + (1-6)**2 } ; ; a = sqrt{ 29 } = 5.39 ; ;

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-(-4))**2 + (-3-6)**2 } ; ; b = sqrt{ 97 } = 9.85 ; ;

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-(-2))**2 + (-3-1)**2 } ; ; c = sqrt{ 20 } = 4.47 ; ;


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 = 5.39 ; ; b = 9.85 ; ; c = 4.47 ; ;

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

p = a+b+c = 5.39+9.85+4.47 = 19.71 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19.71 }{ 2 } = 9.85 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.85 * (9.85-5.39)(9.85-9.85)(9.85-4.47) } ; ; 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 }{ 5.39 } = 0.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1 }{ 9.85 } = 0.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1 }{ 4.47 } = 0.45 ; ;

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{ 5.39**2-9.85**2-4.47**2 }{ 2 * 9.85 * 4.47 } ) = 2° 36'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.85**2-5.39**2-4.47**2 }{ 2 * 5.39 * 4.47 } ) = 175° 14'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.47**2-5.39**2-9.85**2 }{ 2 * 9.85 * 5.39 } ) = 2° 9'40" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1 }{ 9.85 } = 0.1 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.39 }{ 2 * sin 2° 36'9" } = 59.3 ; ;




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