Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 6.32545553203   b = 9.22195444573   c = 15.52441746963

Area: T = 3
Perimeter: p = 31.06882744739
Semiperimeter: s = 15.53441372369

Angle ∠ A = α = 2.4032609469° = 2°24'9″ = 0.04219334459 rad
Angle ∠ B = β = 3.50435316448° = 3°30'13″ = 0.06111481626 rad
Angle ∠ C = γ = 174.0943858886° = 174°5'38″ = 3.03985110451 rad

Height: ha = 0.94986832981
Height: hb = 0.65107913735
Height: hc = 0.38664939758

Median: ma = 12.36993168769
Median: mb = 10.92201648339
Median: mc = 1.5

Inradius: r = 0.19331230524
Circumradius: R = 75.43439298842

Vertex coordinates: A[1; -9] B[5; 6] C[3; 0]
Centroid: CG[3; -1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.15443431896; 0.19331230524]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 177.5977390531° = 177°35'51″ = 0.04219334459 rad
∠ B' = β' = 176.4966468355° = 176°29'47″ = 0.06111481626 rad
∠ C' = γ' = 5.90661411138° = 5°54'22″ = 3.03985110451 rad

Calculate another triangle




How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem

a = |BC| = | beta - gamma | ; ; a**2 = (B_x-C_x)**2 + (B_y-C_y)**2 ; ; a = sqrt{ (B_x-C_x)**2 + (B_y-C_y)**2 } ; ; a = sqrt{ (5-3)**2 + (6-0)**2 } ; ; a = sqrt{ 40 } = 6.32 ; ;

2. We compute side b from coordinates using the Pythagorean theorem

b = |AC| = | alpha - gamma | ; ; b**2 = (A_x-C_x)**2 + (A_y-C_y)**2 ; ; b = sqrt{ (A_x-C_x)**2 + (A_y-C_y)**2 } ; ; b = sqrt{ (1-3)**2 + (-9-0)**2 } ; ; b = sqrt{ 85 } = 9.22 ; ;

3. We compute side c from coordinates using the Pythagorean theorem

c = |AB| = | alpha - beta | ; ; c**2 = (A_x-B_x)**2 + (A_y-B_y)**2 ; ; c = sqrt{ (A_x-B_x)**2 + (A_y-B_y)**2 } ; ; c = sqrt{ (1-5)**2 + (-9-6)**2 } ; ; c = sqrt{ 241 } = 15.52 ; ;


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 = 6.32 ; ; b = 9.22 ; ; c = 15.52 ; ;

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

p = a+b+c = 6.32+9.22+15.52 = 31.07 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 31.07 }{ 2 } = 15.53 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 15.53 * (15.53-6.32)(15.53-9.22)(15.53-15.52) } ; ; T = sqrt{ 9 } = 3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3 }{ 6.32 } = 0.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3 }{ 9.22 } = 0.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3 }{ 15.52 } = 0.39 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 9.22**2+15.52**2-6.32**2 }{ 2 * 9.22 * 15.52 } ) = 2° 24'9" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6.32**2+15.52**2-9.22**2 }{ 2 * 6.32 * 15.52 } ) = 3° 30'13" ; ; gamma = 180° - alpha - beta = 180° - 2° 24'9" - 3° 30'13" = 174° 5'38" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3 }{ 15.53 } = 0.19 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.32 }{ 2 * sin 2° 24'9" } = 75.43 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.22**2+2 * 15.52**2 - 6.32**2 } }{ 2 } = 12.369 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.52**2+2 * 6.32**2 - 9.22**2 } }{ 2 } = 10.92 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.22**2+2 * 6.32**2 - 15.52**2 } }{ 2 } = 1.5 ; ;
Calculate another triangle

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

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