Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 72.79880803318   b = 56.77001807757   c = 17.76438959691

Area: T = 240.86435
Perimeter: p = 147.2622157077
Semiperimeter: s = 73.63110785383

Angle ∠ A = α = 151.4277153742° = 151°25'38″ = 2.64329024097 rad
Angle ∠ B = β = 21.87107587166° = 21°52'15″ = 0.38217167495 rad
Angle ∠ C = γ = 6.70220875413° = 6°42'8″ = 0.11769734944 rad

Height: ha = 6.6177303613
Height: hb = 8.49660399316
Height: hc = 27.11883191367

Median: ma = 20.98443542908
Median: mb = 44.7644166752
Median: mc = 64.64401307239

Inradius: r = 3.27112205876
Circumradius: R = 76.1054722681

Vertex coordinates: A[204.92; 962] B[212.34; 945.86] C[208.76; 1018.57]
Centroid: CG[208.6733333333; 975.4776666667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[8.14994324396; 3.27112205876]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 28.57328462579° = 28°34'22″ = 2.64329024097 rad
∠ B' = β' = 158.1299241283° = 158°7'45″ = 0.38217167495 rad
∠ C' = γ' = 173.2987912459° = 173°17'52″ = 0.11769734944 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{ (212.34-208.76)**2 + (945.86-1018.57)**2 } ; ; a = sqrt{ 5299.561 } = 72.8 ; ;

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{ (204.92-208.76)**2 + (962-1018.57)**2 } ; ; b = sqrt{ 3214.911 } = 56.7 ; ;

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{ (204.92-212.34)**2 + (962-945.86)**2 } ; ; c = sqrt{ 315.556 } = 17.76 ; ;


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 = 72.8 ; ; b = 56.7 ; ; c = 17.76 ; ;

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

p = a+b+c = 72.8+56.7+17.76 = 147.26 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 147.26 }{ 2 } = 73.63 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 73.63 * (73.63-72.8)(73.63-56.7)(73.63-17.76) } ; ; T = sqrt{ 58015.23 } = 240.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 240.86 }{ 72.8 } = 6.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 240.86 }{ 56.7 } = 8.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 240.86 }{ 17.76 } = 27.12 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 56.7**2+17.76**2-72.8**2 }{ 2 * 56.7 * 17.76 } ) = 151° 25'38" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 72.8**2+17.76**2-56.7**2 }{ 2 * 72.8 * 17.76 } ) = 21° 52'15" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 72.8**2+56.7**2-17.76**2 }{ 2 * 72.8 * 56.7 } ) = 6° 42'8" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 240.86 }{ 73.63 } = 3.27 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 72.8 }{ 2 * sin 151° 25'38" } = 76.1 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 56.7**2+2 * 17.76**2 - 72.8**2 } }{ 2 } = 20.984 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.76**2+2 * 72.8**2 - 56.7**2 } }{ 2 } = 44.764 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 56.7**2+2 * 72.8**2 - 17.76**2 } }{ 2 } = 64.64 ; ;
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