Triangle calculator VC

Please enter the coordinates of the three vertices


Right scalene triangle.

Sides: a = 24.18767732449   b = 25.4955097568   c = 8.06222577483

Area: T = 97.5
Perimeter: p = 57.74441285612
Semiperimeter: s = 28.87220642806

Angle ∠ A = α = 71.56550511771° = 71°33'54″ = 1.24990457724 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 18.43549488229° = 18°26'6″ = 0.32217505544 rad

Height: ha = 8.06222577483
Height: hb = 7.64985292704
Height: hc = 24.18767732449

Median: ma = 14.53444418537
Median: mb = 12.7487548784
Median: mc = 24.52203996705

Inradius: r = 3.37769667126
Circumradius: R = 12.7487548784

Vertex coordinates: A[-7; 8] B[-11; 1] C[10; -11]
Centroid: CG[-2.66766666667; -0.66766666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[-0; 3.37769667126]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4354948823° = 108°26'6″ = 1.24990457724 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 161.5655051177° = 161°33'54″ = 0.32217505544 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{ (-11-10)**2 + (1-(-11))**2 } ; ; a = sqrt{ 585 } = 24.19 ; ;

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{ (-7-10)**2 + (8-(-11))**2 } ; ; b = sqrt{ 650 } = 25.5 ; ;

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{ (-7-(-11))**2 + (8-1)**2 } ; ; c = sqrt{ 65 } = 8.06 ; ;


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 = 24.19 ; ; b = 25.5 ; ; c = 8.06 ; ;

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

p = a+b+c = 24.19+25.5+8.06 = 57.74 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57.74 }{ 2 } = 28.87 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.87 * (28.87-24.19)(28.87-25.5)(28.87-8.06) } ; ; T = sqrt{ 9506.25 } = 97.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.5 }{ 24.19 } = 8.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.5 }{ 25.5 } = 7.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.5 }{ 8.06 } = 24.19 ; ;

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{ 24.19**2-25.5**2-8.06**2 }{ 2 * 25.5 * 8.06 } ) = 71° 33'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25.5**2-24.19**2-8.06**2 }{ 2 * 24.19 * 8.06 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.06**2-24.19**2-25.5**2 }{ 2 * 25.5 * 24.19 } ) = 18° 26'6" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.5 }{ 28.87 } = 3.38 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.19 }{ 2 * sin 71° 33'54" } = 12.75 ; ;




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