Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 2.23660679775   b = 5.83109518948   c = 3.60655512755

Area: T = 0.5
Perimeter: p = 11.67325711478
Semiperimeter: s = 5.83662855739

Angle ∠ A = α = 2.72663109939° = 2°43'35″ = 0.04875831033 rad
Angle ∠ B = β = 172.8754983651° = 172°52'30″ = 3.0177237659 rad
Angle ∠ C = γ = 4.3998705355° = 4°23'55″ = 0.07767718913 rad

Height: ha = 0.44772135955
Height: hb = 0.17114985851
Height: hc = 0.27773500981

Median: ma = 4.7176990566
Median: mb = 0.70771067812
Median: mc = 4.03111288741

Inradius: r = 0.08656709278
Circumradius: R = 23.50553185471

Vertex coordinates: A[-1; 3] B[2; 1] C[4; 0]
Centroid: CG[1.66766666667; 1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0.68553674224; 0.08656709278]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.2743689006° = 177°16'25″ = 0.04875831033 rad
∠ B' = β' = 7.12550163489° = 7°7'30″ = 3.0177237659 rad
∠ C' = γ' = 175.6011294645° = 175°36'5″ = 0.07767718913 rad

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How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem

a = |BC| = |B-C| ; ; a**2 = (B_x-C_x)**2 + (B_y-C_y)**2 ; ; a = sqrt{ (B_x-C_x)**2 + (B_y-C_y)**2 } ; ; a = sqrt{ (2-4)**2 + (1-0)**2 } ; ; a = sqrt{ 5 } = 2.24 ; ;

2. We compute side b from coordinates using the Pythagorean theorem

b = |AC| = |A-C| ; ; b**2 = (A_x-C_x)**2 + (A_y-C_y)**2 ; ; b = sqrt{ (A_x-C_x)**2 + (A_y-C_y)**2 } ; ; b = sqrt{ (-1-4)**2 + (3-0)**2 } ; ; b = sqrt{ 34 } = 5.83 ; ;

3. We compute side c from coordinates using the Pythagorean theorem

c = |AB| = |A-B| ; ; c**2 = (A_x-B_x)**2 + (A_y-B_y)**2 ; ; c = sqrt{ (A_x-B_x)**2 + (A_y-B_y)**2 } ; ; c = sqrt{ (-1-2)**2 + (3-1)**2 } ; ; c = sqrt{ 13 } = 3.61 ; ;
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 = 2.24 ; ; b = 5.83 ; ; c = 3.61 ; ;

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

p = a+b+c = 2.24+5.83+3.61 = 11.67 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.67 }{ 2 } = 5.84 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.84 * (5.84-2.24)(5.84-5.83)(5.84-3.61) } ; ; 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 }{ 2.24 } = 0.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.5 }{ 5.83 } = 0.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.5 }{ 3.61 } = 0.28 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 5.83**2+3.61**2-2.24**2 }{ 2 * 5.83 * 3.61 } ) = 2° 43'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.24**2+3.61**2-5.83**2 }{ 2 * 2.24 * 3.61 } ) = 172° 52'30" ; ;
 gamma = 180° - alpha - beta = 180° - 2° 43'35" - 172° 52'30" = 4° 23'55" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.5 }{ 5.84 } = 0.09 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.24 }{ 2 * sin 2° 43'35" } = 23.51 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.83**2+2 * 3.61**2 - 2.24**2 } }{ 2 } = 4.717 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.61**2+2 * 2.24**2 - 5.83**2 } }{ 2 } = 0.707 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.83**2+2 * 2.24**2 - 3.61**2 } }{ 2 } = 4.031 ; ;
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