Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 9.22195444573   b = 3.60655512755   c = 5.83109518948

Area: T = 4.5
Perimeter: p = 18.65660476276
Semiperimeter: s = 9.32880238138

Angle ∠ A = α = 154.6543824058° = 154°39'14″ = 2.69992184306 rad
Angle ∠ B = β = 9.63875381129° = 9°38'15″ = 0.16882067719 rad
Angle ∠ C = γ = 15.7098637829° = 15°42'31″ = 0.27441674511 rad

Height: ha = 0.97661870602
Height: hb = 2.4966150883
Height: hc = 1.54334872663

Median: ma = 1.5
Median: mb = 7.5
Median: mc = 6.36439610307

Inradius: r = 0.48224172933
Circumradius: R = 10.76883234593

Vertex coordinates: A[0; 0] B[-3; 5] C[3; -2]
Centroid: CG[0; 1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[2.84109018383; 0.48224172933]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 25.34661759419° = 25°20'46″ = 2.69992184306 rad
∠ B' = β' = 170.3622461887° = 170°21'45″ = 0.16882067719 rad
∠ C' = γ' = 164.2911362171° = 164°17'29″ = 0.27441674511 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{ (-3-3)**2 + (5-(-2))**2 } ; ; a = sqrt{ 85 } = 9.22 ; ;

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{ (0-3)**2 + (0-(-2))**2 } ; ; b = sqrt{ 13 } = 3.61 ; ;

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{ (0-(-3))**2 + (0-5)**2 } ; ; c = sqrt{ 34 } = 5.83 ; ;


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 = 9.22 ; ; b = 3.61 ; ; c = 5.83 ; ;

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

p = a+b+c = 9.22+3.61+5.83 = 18.66 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.66 }{ 2 } = 9.33 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.33 * (9.33-9.22)(9.33-3.61)(9.33-5.83) } ; ; T = sqrt{ 20.25 } = 4.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.5 }{ 9.22 } = 0.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.5 }{ 3.61 } = 2.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.5 }{ 5.83 } = 1.54 ; ;

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{ 9.22**2-3.61**2-5.83**2 }{ 2 * 3.61 * 5.83 } ) = 154° 39'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.61**2-9.22**2-5.83**2 }{ 2 * 9.22 * 5.83 } ) = 9° 38'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.83**2-9.22**2-3.61**2 }{ 2 * 3.61 * 9.22 } ) = 15° 42'31" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.5 }{ 9.33 } = 0.48 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.22 }{ 2 * sin 154° 39'14" } = 10.77 ; ;




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

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