Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 11.18803398875   b = 5.09990195136   c = 7.81102496759

Area: T = 17.5
Perimeter: p = 24.0989609077
Semiperimeter: s = 12.04548045385

Angle ∠ A = α = 118.4965638618° = 118°29'44″ = 2.06881390431 rad
Angle ∠ B = β = 23.62993777307° = 23°37'46″ = 0.41224104416 rad
Angle ∠ C = γ = 37.87549836511° = 37°52'30″ = 0.66110431689 rad

Height: ha = 3.13304951685
Height: hb = 6.86440647298
Height: hc = 4.48112907977

Median: ma = 3.5
Median: mb = 9.30105376189
Median: mc = 7.76220873481

Inradius: r = 1.45329085918
Circumradius: R = 6.36107533888

Vertex coordinates: A[-3; -4] B[-8; 2] C[2; -3]
Centroid: CG[-3; -1.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.3210933924; 1.45329085918]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 61.50443613818° = 61°30'16″ = 2.06881390431 rad
∠ B' = β' = 156.3710622269° = 156°22'14″ = 0.41224104416 rad
∠ C' = γ' = 142.1255016349° = 142°7'30″ = 0.66110431689 rad

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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{ (-8-2)**2 + (2-(-3))**2 } ; ; a = sqrt{ 125 } = 11.18 ; ;

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{ (-3-2)**2 + (-4-(-3))**2 } ; ; b = sqrt{ 26 } = 5.1 ; ;

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{ (-3-(-8))**2 + (-4-2)**2 } ; ; c = sqrt{ 61 } = 7.81 ; ;


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 = 11.18 ; ; b = 5.1 ; ; c = 7.81 ; ;

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

p = a+b+c = 11.18+5.1+7.81 = 24.09 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.09 }{ 2 } = 12.04 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.04 * (12.04-11.18)(12.04-5.1)(12.04-7.81) } ; ; T = sqrt{ 306.25 } = 17.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.5 }{ 11.18 } = 3.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.5 }{ 5.1 } = 6.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.5 }{ 7.81 } = 4.48 ; ;

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{ 11.18**2-5.1**2-7.81**2 }{ 2 * 5.1 * 7.81 } ) = 118° 29'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.1**2-11.18**2-7.81**2 }{ 2 * 11.18 * 7.81 } ) = 23° 37'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.81**2-11.18**2-5.1**2 }{ 2 * 5.1 * 11.18 } ) = 37° 52'30" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.5 }{ 12.04 } = 1.45 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.18 }{ 2 * sin 118° 29'44" } = 6.36 ; ;




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