Triangle calculator VC

Please enter the coordinates of the three vertices


Acute scalene triangle.

Sides: a = 17.02993863659   b = 23.7769728648   c = 24.59767477525

Area: T = 192.5
Perimeter: p = 65.39658627664
Semiperimeter: s = 32.69879313832

Angle ∠ A = α = 41.18659251657° = 41°11'9″ = 0.71988299996 rad
Angle ∠ B = β = 66.80114094864° = 66°48'5″ = 1.16659045405 rad
Angle ∠ C = γ = 72.01326653479° = 72°46″ = 1.25768581135 rad

Height: ha = 22.60879784513
Height: hb = 16.19770717336
Height: hc = 15.65224758425

Median: ma = 22.63884628453
Median: mb = 17.5
Median: mc = 16.62107701386

Inradius: r = 5.88772225813
Circumradius: R = 12.93303471551

Vertex coordinates: A[-8; -15] B[14; -4] C[1; 7]
Centroid: CG[2.33333333333; -4]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.5233095392; 5.88772225813]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.8144074834° = 138°48'51″ = 0.71988299996 rad
∠ B' = β' = 113.1998590514° = 113°11'55″ = 1.16659045405 rad
∠ C' = γ' = 107.9877334652° = 107°59'14″ = 1.25768581135 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{ (14-1)**2 + (-4-7)**2 } ; ; a = sqrt{ 290 } = 17.03 ; ;

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{ (-8-1)**2 + (-15-7)**2 } ; ; b = sqrt{ 565 } = 23.77 ; ;

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{ (-8-14)**2 + (-15-(-4))**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 = 17.03 ; ; b = 23.77 ; ; c = 24.6 ; ;

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

p = a+b+c = 17.03+23.77+24.6 = 65.4 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65.4 }{ 2 } = 32.7 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.7 * (32.7-17.03)(32.7-23.77)(32.7-24.6) } ; ; T = sqrt{ 37056.25 } = 192.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 192.5 }{ 17.03 } = 22.61 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 192.5 }{ 23.77 } = 16.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 192.5 }{ 24.6 } = 15.65 ; ;

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{ 17.03**2-23.77**2-24.6**2 }{ 2 * 23.77 * 24.6 } ) = 41° 11'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23.77**2-17.03**2-24.6**2 }{ 2 * 17.03 * 24.6 } ) = 66° 48'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24.6**2-17.03**2-23.77**2 }{ 2 * 23.77 * 17.03 } ) = 72° 46" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 192.5 }{ 32.7 } = 5.89 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.03 }{ 2 * sin 41° 11'9" } = 12.93 ; ;




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

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