Triangle calculator VC

Please enter the coordinates of the three vertices


Right scalene triangle.

Sides: a = 17.08880074906   b = 19.10549731745   c = 8.54440037453

Area: T = 73
Perimeter: p = 44.73769844105
Semiperimeter: s = 22.36884922052

Angle ∠ A = α = 63.43549488229° = 63°26'6″ = 1.10771487178 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 26.56550511771° = 26°33'54″ = 0.4643647609 rad

Height: ha = 8.54440037453
Height: hb = 7.64219892698
Height: hc = 17.08880074906

Median: ma = 12.08330459736
Median: mb = 9.55224865873
Median: mc = 17.61439149538

Inradius: r = 3.26435190307
Circumradius: R = 9.55224865873

Vertex coordinates: A[3; 3] B[-5; 6] C[-11; -10]
Centroid: CG[-4.33333333333; -0.33333333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0; 3.26435190307]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5655051177° = 116°33'54″ = 1.10771487178 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 153.4354948823° = 153°26'6″ = 0.4643647609 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{ (-5-(-11))**2 + (6-(-10))**2 } ; ; a = sqrt{ 292 } = 17.09 ; ;

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-(-11))**2 + (3-(-10))**2 } ; ; b = sqrt{ 365 } = 19.1 ; ;

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-(-5))**2 + (3-6)**2 } ; ; c = sqrt{ 73 } = 8.54 ; ;


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 = 17.09 ; ; b = 19.1 ; ; c = 8.54 ; ;

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

p = a+b+c = 17.09+19.1+8.54 = 44.74 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44.74 }{ 2 } = 22.37 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.37 * (22.37-17.09)(22.37-19.1)(22.37-8.54) } ; ; T = sqrt{ 5329 } = 73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 73 }{ 17.09 } = 8.54 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 73 }{ 19.1 } = 7.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 73 }{ 8.54 } = 17.09 ; ;

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{ 17.09**2-19.1**2-8.54**2 }{ 2 * 19.1 * 8.54 } ) = 63° 26'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19.1**2-17.09**2-8.54**2 }{ 2 * 17.09 * 8.54 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.54**2-17.09**2-19.1**2 }{ 2 * 19.1 * 17.09 } ) = 26° 33'54" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 73 }{ 22.37 } = 3.26 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17.09 }{ 2 * sin 63° 26'6" } = 9.55 ; ;




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