Triangle calculator VC

Please enter the coordinates of the three vertices


Right scalene triangle.

Sides: a = 33.43   b = 60.508   c = 69.1298741953

Area: T = 1011.391122
Perimeter: p = 163.0676741953
Semiperimeter: s = 81.53333709765

Angle ∠ A = α = 28.9220164281° = 28°55'13″ = 0.50547520869 rad
Angle ∠ B = β = 61.0879835719° = 61°4'47″ = 1.06660442399 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 60.508
Height: hb = 33.43
Height: hc = 29.26110914484

Median: ma = 62.77442725087
Median: mb = 45.08773531714
Median: mc = 34.56443709765

Inradius: r = 12.40546290235
Circumradius: R = 34.56443709765

Vertex coordinates: A[816.269; -21.696] B[755.761; -55.126] C[755.761; -21.696]
Centroid: CG[775.9330333333; -32.83993333333]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[6.85334201801; 12.40546290235]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0879835719° = 151°4'47″ = 0.50547520869 rad
∠ B' = β' = 118.9220164281° = 118°55'13″ = 1.06660442399 rad
∠ C' = γ' = 90° = 1.57107963268 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{ (755.761-755.761)**2 + (-55.126-(-21.696))**2 } ; ; a = sqrt{ 1117.565 } = 33.43 ; ;

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{ (816.269-755.761)**2 + (-21.696-(-21.696))**2 } ; ; b = sqrt{ 3661.218 } = 60.51 ; ;

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{ (816.269-755.761)**2 + (-21.696-(-55.126))**2 } ; ; c = sqrt{ 4778.783 } = 69.13 ; ;


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 = 33.43 ; ; b = 60.51 ; ; c = 69.13 ; ;

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

p = a+b+c = 33.43+60.51+69.13 = 163.07 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 163.07 }{ 2 } = 81.53 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 81.53 * (81.53-33.43)(81.53-60.51)(81.53-69.13) } ; ; T = sqrt{ 1022912.2 } = 1011.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1011.39 }{ 33.43 } = 60.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1011.39 }{ 60.51 } = 33.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1011.39 }{ 69.13 } = 29.26 ; ;

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{ 33.43**2-60.51**2-69.13**2 }{ 2 * 60.51 * 69.13 } ) = 28° 55'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60.51**2-33.43**2-69.13**2 }{ 2 * 33.43 * 69.13 } ) = 61° 4'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 69.13**2-33.43**2-60.51**2 }{ 2 * 60.51 * 33.43 } ) = 90° ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1011.39 }{ 81.53 } = 12.4 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 33.43 }{ 2 * sin 28° 55'13" } = 34.56 ; ;




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