Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 8.06222577483   b = 14.86660687473   c = 9.48768329805

Area: T = 34.5
Perimeter: p = 32.41551594761
Semiperimeter: s = 16.20875797381

Angle ∠ A = α = 29.2911362171° = 29°17'29″ = 0.51112307123 rad
Angle ∠ B = β = 115.5659965172° = 115°33'36″ = 2.01769018757 rad
Angle ∠ C = γ = 35.14986726572° = 35°8'55″ = 0.61334600656 rad

Height: ha = 8.55883966867
Height: hb = 4.64114422786
Height: hc = 7.27332386184

Median: ma = 11.88004237212
Median: mb = 4.7176990566
Median: mc = 10.97772492001

Inradius: r = 2.12986336737
Circumradius: R = 8.23993885471

Vertex coordinates: A[8; -6] B[-1; -3] C[-2; 5]
Centroid: CG[1.66766666667; -1.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-1.01880421918; 2.12986336737]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.7098637829° = 150°42'31″ = 0.51112307123 rad
∠ B' = β' = 64.44400348282° = 64°26'24″ = 2.01769018757 rad
∠ C' = γ' = 144.8511327343° = 144°51'5″ = 0.61334600656 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{ (-1-(-2))**2 + (-3-5)**2 } ; ; a = sqrt{ 65 } = 8.06 ; ;

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-(-2))**2 + (-6-5)**2 } ; ; b = sqrt{ 221 } = 14.87 ; ;

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-(-1))**2 + (-6-(-3))**2 } ; ; c = sqrt{ 90 } = 9.49 ; ;


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 = 8.06 ; ; b = 14.87 ; ; c = 9.49 ; ;

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

p = a+b+c = 8.06+14.87+9.49 = 32.42 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.42 }{ 2 } = 16.21 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.21 * (16.21-8.06)(16.21-14.87)(16.21-9.49) } ; ; T = sqrt{ 1190.25 } = 34.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.5 }{ 8.06 } = 8.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.5 }{ 14.87 } = 4.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.5 }{ 9.49 } = 7.27 ; ;

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{ 8.06**2-14.87**2-9.49**2 }{ 2 * 14.87 * 9.49 } ) = 29° 17'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14.87**2-8.06**2-9.49**2 }{ 2 * 8.06 * 9.49 } ) = 115° 33'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.49**2-8.06**2-14.87**2 }{ 2 * 14.87 * 8.06 } ) = 35° 8'55" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.5 }{ 16.21 } = 2.13 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.06 }{ 2 * sin 29° 17'29" } = 8.24 ; ;




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

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