Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 0.94333981132   b = 2.91554759474   c = 1.97223082923

Area: T = 0.025
Perimeter: p = 5.8311182353
Semiperimeter: s = 2.91655911765

Angle ∠ A = α = 0.49882116126° = 0°29'54″ = 0.0098695433 rad
Angle ∠ B = β = 178.4660161711° = 178°27'37″ = 3.11547174055 rad
Angle ∠ C = γ = 1.0421626676° = 1°2'30″ = 0.01881798151 rad

Height: ha = 0.0532999894
Height: hb = 0.01771498585
Height: hc = 0.02553510063

Median: ma = 2.4443869882
Median: mb = 0.5154781507
Median: mc = 1.92993781382

Inradius: r = 0.00985745904
Circumradius: R = 54.24774423361

Vertex coordinates: A[2.5; 2] B[4.2; 3] C[5; 3.5]
Centroid: CG[3.9; 2.83333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0.31989747614; 0.00985745904]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.5021788387° = 179°30'6″ = 0.0098695433 rad
∠ B' = β' = 1.54398382886° = 1°32'23″ = 3.11547174055 rad
∠ C' = γ' = 178.9588373324° = 178°57'30″ = 0.01881798151 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{ (4.2-5)**2 + (3-3.5)**2 } ; ; a = sqrt{ 0.89 } = 0.94 ; ;

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{ (2.5-5)**2 + (2-3.5)**2 } ; ; b = sqrt{ 8.5 } = 2.92 ; ;

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{ (2.5-4.2)**2 + (2-3)**2 } ; ; c = sqrt{ 3.89 } = 1.97 ; ;


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 = 0.94 ; ; b = 2.92 ; ; c = 1.97 ; ;

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

p = a+b+c = 0.94+2.92+1.97 = 5.83 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.83 }{ 2 } = 2.92 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.92 * (2.92-0.94)(2.92-2.92)(2.92-1.97) } ; ; T = sqrt{ 0 } = 0.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.03 }{ 0.94 } = 0.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.03 }{ 2.92 } = 0.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.03 }{ 1.97 } = 0.03 ; ;

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{ 0.94**2-2.92**2-1.97**2 }{ 2 * 2.92 * 1.97 } ) = 0° 29'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2.92**2-0.94**2-1.97**2 }{ 2 * 0.94 * 1.97 } ) = 178° 27'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1.97**2-0.94**2-2.92**2 }{ 2 * 2.92 * 0.94 } ) = 1° 2'30" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.03 }{ 2.92 } = 0.01 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.94 }{ 2 * sin 0° 29'54" } = 54.25 ; ;




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