Triangle calculator VC

Please enter the coordinates of the three vertices


Acute scalene triangle.

Sides: a = 6.08327625303   b = 6.40331242374   c = 4.4722135955

Area: T = 13
Perimeter: p = 16.95880227227
Semiperimeter: s = 8.47990113614

Angle ∠ A = α = 65.22548594312° = 65°13'29″ = 1.13883885512 rad
Angle ∠ B = β = 72.89772710309° = 72°53'50″ = 1.27222973952 rad
Angle ∠ C = γ = 41.87878695379° = 41°52'40″ = 0.73109067072 rad

Height: ha = 4.27443736699
Height: hb = 4.06105178091
Height: hc = 5.81437767415

Median: ma = 4.61097722286
Median: mb = 4.27220018727
Median: mc = 5.83109518948

Inradius: r = 1.53331976154
Circumradius: R = 3.35496886723

Vertex coordinates: A[2; 5] B[4; 1] C[-2; 0]
Centroid: CG[1.33333333333; 2]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[0.47217531124; 1.53331976154]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.7755140569° = 114°46'31″ = 1.13883885512 rad
∠ B' = β' = 107.1032728969° = 107°6'10″ = 1.27222973952 rad
∠ C' = γ' = 138.1222130462° = 138°7'20″ = 0.73109067072 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-(-2))**2 + (1-0)**2 } ; ; a = sqrt{ 37 } = 6.08 ; ;

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

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{ (2-4)**2 + (5-1)**2 } ; ; c = sqrt{ 20 } = 4.47 ; ;


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 = 6.08 ; ; b = 6.4 ; ; c = 4.47 ; ;

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

p = a+b+c = 6.08+6.4+4.47 = 16.96 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.96 }{ 2 } = 8.48 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.48 * (8.48-6.08)(8.48-6.4)(8.48-4.47) } ; ; T = sqrt{ 169 } = 13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13 }{ 6.08 } = 4.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13 }{ 6.4 } = 4.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13 }{ 4.47 } = 5.81 ; ;

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{ 6.08**2-6.4**2-4.47**2 }{ 2 * 6.4 * 4.47 } ) = 65° 13'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6.4**2-6.08**2-4.47**2 }{ 2 * 6.08 * 4.47 } ) = 72° 53'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.47**2-6.08**2-6.4**2 }{ 2 * 6.4 * 6.08 } ) = 41° 52'40" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13 }{ 8.48 } = 1.53 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.08 }{ 2 * sin 65° 13'29" } = 3.35 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.