Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 10.77703296143   b = 8.24662112512   c = 2.82884271247

Area: T = 6
Perimeter: p = 21.84549679903
Semiperimeter: s = 10.92224839951

Angle ∠ A = α = 149.0366243468° = 149°2'10″ = 2.60111731533 rad
Angle ∠ B = β = 23.19985905136° = 23°11'55″ = 0.40548917863 rad
Angle ∠ C = γ = 7.76551660184° = 7°45'55″ = 0.1365527714 rad

Height: ha = 1.11441720291
Height: hb = 1.45552137502
Height: hc = 4.24326406871

Median: ma = 3
Median: mb = 6.70882039325
Median: mc = 9.48768329805

Inradius: r = 0.54993255932
Circumradius: R = 10.46768789787

Vertex coordinates: A[2; 4] B[4; 6] C[0; -4]
Centroid: CG[2; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.28217597175; 0.54993255932]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 30.96437565321° = 30°57'50″ = 2.60111731533 rad
∠ B' = β' = 156.8011409486° = 156°48'5″ = 0.40548917863 rad
∠ C' = γ' = 172.2354833982° = 172°14'5″ = 0.1365527714 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{ (4-0)**2 + (6-(-4))**2 } ; ; a = sqrt{ 116 } = 10.77 ; ;

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{ (2-0)**2 + (4-(-4))**2 } ; ; b = sqrt{ 68 } = 8.25 ; ;

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{ (2-4)**2 + (4-6)**2 } ; ; c = sqrt{ 8 } = 2.83 ; ;


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 = 10.77 ; ; b = 8.25 ; ; c = 2.83 ; ;

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

p = a+b+c = 10.77+8.25+2.83 = 21.84 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.84 }{ 2 } = 10.92 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.92 * (10.92-10.77)(10.92-8.25)(10.92-2.83) } ; ; T = sqrt{ 36 } = 6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6 }{ 10.77 } = 1.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6 }{ 8.25 } = 1.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6 }{ 2.83 } = 4.24 ; ;

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{ 10.77**2-8.25**2-2.83**2 }{ 2 * 8.25 * 2.83 } ) = 149° 2'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.25**2-10.77**2-2.83**2 }{ 2 * 10.77 * 2.83 } ) = 23° 11'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2.83**2-10.77**2-8.25**2 }{ 2 * 8.25 * 10.77 } ) = 7° 45'55" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6 }{ 10.92 } = 0.55 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.77 }{ 2 * sin 149° 2'10" } = 10.47 ; ;




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