Triangle calculator VC

Please enter the coordinates of the three vertices


Right scalene triangle.

Sides: a = 13.4166407865   b = 28.01878514522   c = 24.59767477525

Area: T = 165
Perimeter: p = 66.03110070697
Semiperimeter: s = 33.01655035349

Angle ∠ A = α = 28.6110459666° = 28°36'38″ = 0.49993467217 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 61.3989540334° = 61°23'22″ = 1.07114496051 rad

Height: ha = 24.59767477525
Height: hb = 11.77882050691
Height: hc = 13.4166407865

Median: ma = 25.4955097568
Median: mb = 14.00989257261
Median: mc = 18.22002747232

Inradius: r = 4.99876520826
Circumradius: R = 14.00989257261

Vertex coordinates: A[-10; 5] B[12; 16] C[18; 4]
Centroid: CG[6.66766666667; 8.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0; 4.99876520826]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.3989540334° = 151°23'22″ = 0.49993467217 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 118.6110459666° = 118°36'38″ = 1.07114496051 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{ (12-18)**2 + (16-4)**2 } ; ; a = sqrt{ 180 } = 13.42 ; ;

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{ (-10-18)**2 + (5-4)**2 } ; ; b = sqrt{ 785 } = 28.02 ; ;

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{ (-10-12)**2 + (5-16)**2 } ; ; c = sqrt{ 605 } = 24.6 ; ;


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 = 13.42 ; ; b = 28.02 ; ; c = 24.6 ; ;

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

p = a+b+c = 13.42+28.02+24.6 = 66.03 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66.03 }{ 2 } = 33.02 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.02 * (33.02-13.42)(33.02-28.02)(33.02-24.6) } ; ; T = sqrt{ 27225 } = 165 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 165 }{ 13.42 } = 24.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 165 }{ 28.02 } = 11.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 165 }{ 24.6 } = 13.42 ; ;

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{ 13.42**2-28.02**2-24.6**2 }{ 2 * 28.02 * 24.6 } ) = 28° 36'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28.02**2-13.42**2-24.6**2 }{ 2 * 13.42 * 24.6 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24.6**2-13.42**2-28.02**2 }{ 2 * 28.02 * 13.42 } ) = 61° 23'22" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 165 }{ 33.02 } = 5 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13.42 }{ 2 * sin 28° 36'38" } = 14.01 ; ;




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

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