Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 15.7911041036   b = 13.43995994716   c = 28.79327473681

Area: T = 34.45552145004
Perimeter: p = 57.98333878757
Semiperimeter: s = 28.99216939379

Angle ∠ A = α = 10.28989087095° = 10°17'20″ = 0.18795753334 rad
Angle ∠ B = β = 8.71774729185° = 8°43'3″ = 0.15221486049 rad
Angle ∠ C = γ = 160.9943618372° = 160°59'37″ = 2.81098687153 rad

Height: ha = 4.36438939854
Height: hb = 5.14327230453
Height: hc = 2.39333259345

Median: ma = 21.02325245689
Median: mb = 22.23329107969
Median: mc = 2.68328243047

Inradius: r = 1.18884512362
Circumradius: R = 44.2054932992

Vertex coordinates: A[401057.786; 487138.255] B[401029.316; 487142.554] C[401045.107; 487142.59]
Centroid: CG[401044.0769667; 487141.133]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[7.75107545258; 1.18884512362]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.711109129° = 169°42'40″ = 0.18795753334 rad
∠ B' = β' = 171.2832527082° = 171°16'57″ = 0.15221486049 rad
∠ C' = γ' = 19.0066381628° = 19°23″ = 2.81098687153 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{ (401029.316-401045.107)**2 + (487142.554-487142.59)**2 } ; ; a = sqrt{ 249.357 } = 15.79 ; ;

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{ (401057.786-401045.107)**2 + (487138.255-487142.59)**2 } ; ; b = sqrt{ 179.549 } = 13.4 ; ;

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{ (401057.786-401029.316)**2 + (487138.255-487142.554)**2 } ; ; c = sqrt{ 829.022 } = 28.79 ; ;


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 = 15.79 ; ; b = 13.4 ; ; c = 28.79 ; ;

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

p = a+b+c = 15.79+13.4+28.79 = 57.98 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57.98 }{ 2 } = 28.99 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.99 * (28.99-15.79)(28.99-13.4)(28.99-28.79) } ; ; T = sqrt{ 1187.16 } = 34.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.46 }{ 15.79 } = 4.36 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.46 }{ 13.4 } = 5.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.46 }{ 28.79 } = 2.39 ; ;

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{ 15.79**2-13.4**2-28.79**2 }{ 2 * 13.4 * 28.79 } ) = 10° 17'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.4**2-15.79**2-28.79**2 }{ 2 * 15.79 * 28.79 } ) = 8° 43'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28.79**2-15.79**2-13.4**2 }{ 2 * 13.4 * 15.79 } ) = 160° 59'37" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.46 }{ 28.99 } = 1.19 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15.79 }{ 2 * sin 10° 17'20" } = 44.2 ; ;




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