Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 19.64768827044   b = 8.24662112512   c = 11.4021754251

Area: T = 1
Perimeter: p = 39.29548482066
Semiperimeter: s = 19.64774241033

Angle ∠ A = α = 178.7811124765° = 178°46'52″ = 3.12203192676 rad
Angle ∠ B = β = 0.51215558666° = 0°30'42″ = 0.00989283342 rad
Angle ∠ C = γ = 0.70773193685° = 0°42'26″ = 0.01223450518 rad

Height: ha = 0.10217973197
Height: hb = 0.2432535625
Height: hc = 0.17554116039

Median: ma = 1.58111388301
Median: mb = 15.52441746963
Median: mc = 13.9466325681

Inradius: r = 0.05108972573
Circumradius: R = 461.8066236424

Vertex coordinates: A[0; -9] B[-3; -20] C[2; -1]
Centroid: CG[-0.33333333333; -10]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[5.77004928184; 0.05108972573]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1.21988752351° = 1°13'8″ = 3.12203192676 rad
∠ B' = β' = 179.4888444133° = 179°29'18″ = 0.00989283342 rad
∠ C' = γ' = 179.2932680631° = 179°17'34″ = 0.01223450518 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{ (-3-2)**2 + (-20-(-1))**2 } ; ; a = sqrt{ 386 } = 19.65 ; ;

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{ (0-2)**2 + (-9-(-1))**2 } ; ; b = sqrt{ 68 } = 8.25 ; ;

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 + (-9-(-20))**2 } ; ; c = sqrt{ 130 } = 11.4 ; ;


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 = 19.65 ; ; b = 8.25 ; ; c = 11.4 ; ;

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

p = a+b+c = 19.65+8.25+11.4 = 39.29 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39.29 }{ 2 } = 19.65 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.65 * (19.65-19.65)(19.65-8.25)(19.65-11.4) } ; ; T = sqrt{ 1 } = 1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1 }{ 19.65 } = 0.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1 }{ 8.25 } = 0.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1 }{ 11.4 } = 0.18 ; ;

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{ 19.65**2-8.25**2-11.4**2 }{ 2 * 8.25 * 11.4 } ) = 178° 46'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.25**2-19.65**2-11.4**2 }{ 2 * 19.65 * 11.4 } ) = 0° 30'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.4**2-19.65**2-8.25**2 }{ 2 * 8.25 * 19.65 } ) = 0° 42'26" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1 }{ 19.65 } = 0.05 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19.65 }{ 2 * sin 178° 46'52" } = 461.81 ; ;




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

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