Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 6.32545553203   b = 9.22195444573   c = 15.52441746963

Area: T = 3
Perimeter: p = 31.06882744739
Semiperimeter: s = 15.53441372369

Angle ∠ A = α = 2.4032609469° = 2°24'9″ = 0.04219334459 rad
Angle ∠ B = β = 3.50435316448° = 3°30'13″ = 0.06111481626 rad
Angle ∠ C = γ = 174.0943858886° = 174°5'38″ = 3.03985110451 rad

Height: ha = 0.94986832981
Height: hb = 0.65107913735
Height: hc = 0.38664939758

Median: ma = 12.36993168769
Median: mb = 10.92201648339
Median: mc = 1.5

Inradius: r = 0.19331230524
Circumradius: R = 75.43439298842

Vertex coordinates: A[1; -9] B[5; 6] C[3; 0]
Centroid: CG[3; -1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.15443431896; 0.19331230524]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.5977390531° = 177°35'51″ = 0.04219334459 rad
∠ B' = β' = 176.4966468355° = 176°29'47″ = 0.06111481626 rad
∠ C' = γ' = 5.90661411138° = 5°54'22″ = 3.03985110451 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{ (5-3)**2 + (6-0)**2 } ; ; a = sqrt{ 40 } = 6.32 ; ;

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{ (1-3)**2 + (-9-0)**2 } ; ; b = sqrt{ 85 } = 9.22 ; ;

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{ (1-5)**2 + (-9-6)**2 } ; ; c = sqrt{ 241 } = 15.52 ; ;


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 = 6.32 ; ; b = 9.22 ; ; c = 15.52 ; ;

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

p = a+b+c = 6.32+9.22+15.52 = 31.07 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.07 }{ 2 } = 15.53 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.53 * (15.53-6.32)(15.53-9.22)(15.53-15.52) } ; ; T = sqrt{ 9 } = 3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3 }{ 6.32 } = 0.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3 }{ 9.22 } = 0.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3 }{ 15.52 } = 0.39 ; ;

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{ 6.32**2-9.22**2-15.52**2 }{ 2 * 9.22 * 15.52 } ) = 2° 24'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.22**2-6.32**2-15.52**2 }{ 2 * 6.32 * 15.52 } ) = 3° 30'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15.52**2-6.32**2-9.22**2 }{ 2 * 9.22 * 6.32 } ) = 174° 5'38" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3 }{ 15.53 } = 0.19 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.32 }{ 2 * sin 2° 24'9" } = 75.43 ; ;




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