Triangle calculator VC

Please enter the coordinates of the three vertices


Right scalene triangle.

Sides: a = 11.18803398875   b = 8.944427191   c = 14.31878210633

Area: T = 50
Perimeter: p = 34.44224328608
Semiperimeter: s = 17.22112164304

Angle ∠ A = α = 51.34401917459° = 51°20'25″ = 0.89660553846 rad
Angle ∠ B = β = 38.66598082541° = 38°39'35″ = 0.67547409422 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 8.944427191
Height: hb = 11.18803398875
Height: hc = 6.98443029577

Median: ma = 10.54875115549
Median: mb = 12.04215945788
Median: mc = 7.15989105316

Inradius: r = 2.90333953671
Circumradius: R = 7.15989105316

Vertex coordinates: A[10; 2] B[-4; 5] C[6; 10]
Centroid: CG[4; 5.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.62992442089; 2.90333953671]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.6659808254° = 128°39'35″ = 0.89660553846 rad
∠ B' = β' = 141.3440191746° = 141°20'25″ = 0.67547409422 rad
∠ C' = γ' = 90° = 1.57107963268 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{ (-4-6)**2 + (5-10)**2 } ; ; a = sqrt{ 125 } = 11.18 ; ;

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{ (10-6)**2 + (2-10)**2 } ; ; b = sqrt{ 80 } = 8.94 ; ;

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{ (10-(-4))**2 + (2-5)**2 } ; ; c = sqrt{ 205 } = 14.32 ; ;


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 = 11.18 ; ; b = 8.94 ; ; c = 14.32 ; ;

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

p = a+b+c = 11.18+8.94+14.32 = 34.44 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34.44 }{ 2 } = 17.22 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.22 * (17.22-11.18)(17.22-8.94)(17.22-14.32) } ; ; T = sqrt{ 2500 } = 50 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50 }{ 11.18 } = 8.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50 }{ 8.94 } = 11.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50 }{ 14.32 } = 6.98 ; ;

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{ 11.18**2-8.94**2-14.32**2 }{ 2 * 8.94 * 14.32 } ) = 51° 20'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.94**2-11.18**2-14.32**2 }{ 2 * 11.18 * 14.32 } ) = 38° 39'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14.32**2-11.18**2-8.94**2 }{ 2 * 8.94 * 11.18 } ) = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50 }{ 17.22 } = 2.9 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.18 }{ 2 * sin 51° 20'25" } = 7.16 ; ;




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