Triangle calculator VC

Please enter the coordinates of the three vertices


Right scalene triangle.

Sides: a = 12.64991106407   b = 14.14221356237   c = 6.32545553203

Area: T = 40
Perimeter: p = 33.11658015847
Semiperimeter: s = 16.55879007924

Angle ∠ A = α = 63.43549488229° = 63°26'6″ = 1.10771487178 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 26.56550511771° = 26°33'54″ = 0.4643647609 rad

Height: ha = 6.32545553203
Height: hb = 5.65768542495
Height: hc = 12.64991106407

Median: ma = 8.944427191
Median: mb = 7.07110678119
Median: mc = 13.03884048104

Inradius: r = 2.41657651686
Circumradius: R = 7.07110678119

Vertex coordinates: A[-3; 8] B[3; 10] C[7; -2]
Centroid: CG[2.33333333333; 5.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0; 2.41657651686]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5655051177° = 116°33'54″ = 1.10771487178 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 153.4354948823° = 153°26'6″ = 0.4643647609 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{ (3-7)**2 + (10-(-2))**2 } ; ; a = sqrt{ 160 } = 12.65 ; ;

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{ (-3-7)**2 + (8-(-2))**2 } ; ; b = sqrt{ 200 } = 14.14 ; ;

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{ (-3-3)**2 + (8-10)**2 } ; ; c = sqrt{ 40 } = 6.32 ; ;


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 = 12.65 ; ; b = 14.14 ; ; c = 6.32 ; ;

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

p = a+b+c = 12.65+14.14+6.32 = 33.12 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.12 }{ 2 } = 16.56 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.56 * (16.56-12.65)(16.56-14.14)(16.56-6.32) } ; ; T = sqrt{ 1600 } = 40 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40 }{ 12.65 } = 6.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40 }{ 14.14 } = 5.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40 }{ 6.32 } = 12.65 ; ;

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{ 12.65**2-14.14**2-6.32**2 }{ 2 * 14.14 * 6.32 } ) = 63° 26'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14.14**2-12.65**2-6.32**2 }{ 2 * 12.65 * 6.32 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.32**2-12.65**2-14.14**2 }{ 2 * 14.14 * 12.65 } ) = 26° 33'54" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40 }{ 16.56 } = 2.42 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.65 }{ 2 * sin 63° 26'6" } = 7.07 ; ;




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

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