Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 949.7177444146   b = 445.6854850611   c = 504.0844356151

Area: T = 2349.839852
Perimeter: p = 1899.487665091
Semiperimeter: s = 949.7433325454

Angle ∠ A = α = 178.8011353189° = 178°48'5″ = 3.12106723202 rad
Angle ∠ B = β = 0.56224708082° = 0°33'45″ = 0.01098169675 rad
Angle ∠ C = γ = 0.63661760032° = 0°38'10″ = 0.01111033659 rad

Height: ha = 4.94985002818
Height: hb = 10.54548435897
Height: hc = 9.32331955776

Median: ma = 29.61876663665
Median: mb = 726.8932966261
Median: mc = 697.6921798261

Inradius: r = 2.47441827155
Circumradius: R = 22700.08656999

Vertex coordinates: A[-66.265; 412.3] B[-99.311; 915.3] C[-46.357; -32.94]
Centroid: CG[-70.64443333333; 431.5533333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[252.023316513; 2.47441827155]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1.19986468113° = 1°11'55″ = 3.12106723202 rad
∠ B' = β' = 179.4387529192° = 179°26'15″ = 0.01098169675 rad
∠ C' = γ' = 179.3643823997° = 179°21'50″ = 0.01111033659 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{ (-99.311-(-46.357))**2 + (915.3-(-32.94))**2 } ; ; a = sqrt{ 901963.224 } = 949.72 ; ;

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{ (-66.265-(-46.357))**2 + (412.3-(-32.94))**2 } ; ; b = sqrt{ 198634.986 } = 445.68 ; ;

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{ (-66.265-(-99.311))**2 + (412.3-915.3)**2 } ; ; c = sqrt{ 254101.038 } = 504.08 ; ;


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 = 949.72 ; ; b = 445.68 ; ; c = 504.08 ; ;

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

p = a+b+c = 949.72+445.68+504.08 = 1899.49 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1899.49 }{ 2 } = 949.74 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 949.74 * (949.74-949.72)(949.74-445.68)(949.74-504.08) } ; ; T = sqrt{ 5521741.07 } = 2349.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2349.84 }{ 949.72 } = 4.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2349.84 }{ 445.68 } = 10.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2349.84 }{ 504.08 } = 9.32 ; ;

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{ 949.72**2-445.68**2-504.08**2 }{ 2 * 445.68 * 504.08 } ) = 178° 48'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 445.68**2-949.72**2-504.08**2 }{ 2 * 949.72 * 504.08 } ) = 0° 33'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 504.08**2-949.72**2-445.68**2 }{ 2 * 445.68 * 949.72 } ) = 0° 38'10" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2349.84 }{ 949.74 } = 2.47 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 949.72 }{ 2 * sin 178° 48'5" } = 22700.09 ; ;




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