Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 12.64991106407   b = 5.65768542495   c = 17.889854382

Area: T = 16
Perimeter: p = 36.19545087102
Semiperimeter: s = 18.09772543551

Angle ∠ A = α = 18.43549488229° = 18°26'6″ = 0.32217505544 rad
Angle ∠ B = β = 8.13301023542° = 8°7'48″ = 0.14218970546 rad
Angle ∠ C = γ = 153.4354948823° = 153°26'6″ = 2.67879450446 rad

Height: ha = 2.53298221281
Height: hb = 5.65768542495
Height: hc = 1.7898854382

Median: ma = 11.66219037897
Median: mb = 15.23215462117
Median: mc = 4

Inradius: r = 0.88441120142
Circumradius: R = 20

Vertex coordinates: A[-10; -3] B[6; 5] C[-6; 1]
Centroid: CG[-3.33333333333; 1]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[6.18987840996; 0.88441120142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5655051177° = 161°33'54″ = 0.32217505544 rad
∠ B' = β' = 171.8769897646° = 171°52'12″ = 0.14218970546 rad
∠ C' = γ' = 26.56550511771° = 26°33'54″ = 2.67879450446 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{ (6-(-6))**2 + (5-1)**2 } ; ; a = sqrt{ 160 } = 12.65 ; ;

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{ (-10-(-6))**2 + (-3-1)**2 } ; ; b = sqrt{ 32 } = 5.66 ; ;

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{ (-10-6)**2 + (-3-5)**2 } ; ; c = sqrt{ 320 } = 17.89 ; ;


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 = 12.65 ; ; b = 5.66 ; ; c = 17.89 ; ;

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

p = a+b+c = 12.65+5.66+17.89 = 36.19 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 36.19 }{ 2 } = 18.1 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.1 * (18.1-12.65)(18.1-5.66)(18.1-17.89) } ; ; T = sqrt{ 256 } = 16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16 }{ 12.65 } = 2.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16 }{ 5.66 } = 5.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16 }{ 17.89 } = 1.79 ; ;

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{ 12.65**2-5.66**2-17.89**2 }{ 2 * 5.66 * 17.89 } ) = 18° 26'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.66**2-12.65**2-17.89**2 }{ 2 * 12.65 * 17.89 } ) = 8° 7'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17.89**2-12.65**2-5.66**2 }{ 2 * 5.66 * 12.65 } ) = 153° 26'6" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16 }{ 18.1 } = 0.88 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12.65 }{ 2 * sin 18° 26'6" } = 20 ; ;




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