Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 10.63301458127   b = 4.4722135955   c = 6.40331242374

Area: T = 6
Perimeter: p = 21.50554060052
Semiperimeter: s = 10.75327030026

Angle ∠ A = α = 155.2254859431° = 155°13'29″ = 2.7099184878 rad
Angle ∠ B = β = 10.15442665802° = 10°9'15″ = 0.17772253849 rad
Angle ∠ C = γ = 14.62108739886° = 14°37'15″ = 0.25551823906 rad

Height: ha = 1.12988650421
Height: hb = 2.6833281573
Height: hc = 1.87440851427

Median: ma = 1.5
Median: mb = 8.48552813742
Median: mc = 7.5

Inradius: r = 0.55879992304
Circumradius: R = 12.68333771353

Vertex coordinates: A[0; 0] B[-4; 5] C[4; -2]
Centroid: CG[0; 1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.1155495703; 0.55879992304]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 24.77551405688° = 24°46'31″ = 2.7099184878 rad
∠ B' = β' = 169.846573342° = 169°50'45″ = 0.17772253849 rad
∠ C' = γ' = 165.3799126011° = 165°22'45″ = 0.25551823906 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{ (-4-4)**2 + (5-(-2))**2 } ; ; a = sqrt{ 113 } = 10.63 ; ;

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{ (0-4)**2 + (0-(-2))**2 } ; ; b = sqrt{ 20 } = 4.47 ; ;

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{ (0-(-4))**2 + (0-5)**2 } ; ; c = sqrt{ 41 } = 6.4 ; ;


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 = 10.63 ; ; b = 4.47 ; ; c = 6.4 ; ;

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

p = a+b+c = 10.63+4.47+6.4 = 21.51 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.51 }{ 2 } = 10.75 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.75 * (10.75-10.63)(10.75-4.47)(10.75-6.4) } ; ; 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 }{ 10.63 } = 1.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6 }{ 4.47 } = 2.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6 }{ 6.4 } = 1.87 ; ;

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{ 10.63**2-4.47**2-6.4**2 }{ 2 * 4.47 * 6.4 } ) = 155° 13'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.47**2-10.63**2-6.4**2 }{ 2 * 10.63 * 6.4 } ) = 10° 9'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.4**2-10.63**2-4.47**2 }{ 2 * 4.47 * 10.63 } ) = 14° 37'15" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6 }{ 10.75 } = 0.56 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.63 }{ 2 * sin 155° 13'29" } = 12.68 ; ;




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