Triangle calculator SSA

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Triangle has two solutions with side c=77.52224036152 and with side c=16.44768584634

#1 Obtuse scalene triangle.

Sides: a = 50   b = 35   c = 77.52224036152

Area: T = 662.8565589886
Perimeter: p = 162.5222403615
Semiperimeter: s = 81.26112018076

Angle ∠ A = α = 29.24986185511° = 29°14'55″ = 0.51104846954 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 130.7511381449° = 130°45'5″ = 2.28220421078 rad

Height: ha = 26.51442235954
Height: hb = 37.87774622792
Height: hc = 17.10110071663

Median: ma = 54.70224819468
Median: mb = 62.83879784139
Median: mc = 18.97554903607

Inradius: r = 8.15770980387
Circumradius: R = 51.16765770029

Vertex coordinates: A[77.52224036152; 0] B[0; 0] C[46.98546310393; 17.10110071663]
Centroid: CG[41.50223448848; 5.77003357221]
Coordinates of the circumscribed circle: U[38.76112018076; -33.44004167133]
Coordinates of the inscribed circle: I[46.26112018076; 8.15770980387]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.7511381449° = 150°45'5″ = 0.51104846954 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 49.24986185511° = 49°14'55″ = 2.28220421078 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 50 ; ; b = 35 ; ; beta = 20° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 35**2 = 50**2 + c**2 -2 * 50 * c * cos (20° ) ; ; ; ; c**2 -93.969c +1275 =0 ; ; p=1; q=-93.969; r=1275 ; ; D = q**2 - 4pr = 93.969**2 - 4 * 1 * 1275 = 3730.22221559 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 93.97 ± sqrt{ 3730.22 } }{ 2 } ; ; c_{1,2} = 46.98463104 ± 30.5377725759 ; ; c_{1} = 77.5224036159 ; ;
c_{2} = 16.4468584641 ; ; ; ; (c -77.5224036159) (c -16.4468584641) = 0 ; ; ; ; c>0 ; ;


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 = 50 ; ; b = 35 ; ; c = 77.52 ; ;

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

p = a+b+c = 50+35+77.52 = 162.52 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 162.52 }{ 2 } = 81.26 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 81.26 * (81.26-50)(81.26-35)(81.26-77.52) } ; ; T = sqrt{ 439377.53 } = 662.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 662.86 }{ 50 } = 26.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 662.86 }{ 35 } = 37.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 662.86 }{ 77.52 } = 17.1 ; ;

6. 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{ 50**2-35**2-77.52**2 }{ 2 * 35 * 77.52 } ) = 29° 14'55" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 35**2-50**2-77.52**2 }{ 2 * 50 * 77.52 } ) = 20° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 77.52**2-50**2-35**2 }{ 2 * 35 * 50 } ) = 130° 45'5" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 662.86 }{ 81.26 } = 8.16 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 29° 14'55" } = 51.17 ; ;





#2 Obtuse scalene triangle.

Sides: a = 50   b = 35   c = 16.44768584634

Area: T = 140.6298922222
Perimeter: p = 101.4476858463
Semiperimeter: s = 50.72334292317

Angle ∠ A = α = 150.7511381449° = 150°45'5″ = 2.63111079582 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 9.24986185511° = 9°14'55″ = 0.1611418845 rad

Height: ha = 5.62551568889
Height: hb = 8.03659384127
Height: hc = 17.10110071663

Median: ma = 11.07992407979
Median: mb = 32.84881289674
Median: mc = 42.36659676117

Inradius: r = 2.77224648028
Circumradius: R = 51.16765770029

Vertex coordinates: A[16.44768584634; 0] B[0; 0] C[46.98546310393; 17.10110071663]
Centroid: CG[21.14438298342; 5.77003357221]
Coordinates of the circumscribed circle: U[8.22334292317; 50.50114238795]
Coordinates of the inscribed circle: I[15.72334292317; 2.77224648028]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 29.24986185511° = 29°14'55″ = 2.63111079582 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 170.7511381449° = 170°45'5″ = 0.1611418845 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 50 ; ; b = 35 ; ; beta = 20° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 35**2 = 50**2 + c**2 -2 * 50 * c * cos (20° ) ; ; ; ; c**2 -93.969c +1275 =0 ; ; p=1; q=-93.969; r=1275 ; ; D = q**2 - 4pr = 93.969**2 - 4 * 1 * 1275 = 3730.22221559 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 93.97 ± sqrt{ 3730.22 } }{ 2 } ; ; c_{1,2} = 46.98463104 ± 30.5377725759 ; ; c_{1} = 77.5224036159 ; ; : Nr. 1
c_{2} = 16.4468584641 ; ; ; ; (c -77.5224036159) (c -16.4468584641) = 0 ; ; ; ; c>0 ; ; : Nr. 1


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 = 50 ; ; b = 35 ; ; c = 16.45 ; ;

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

p = a+b+c = 50+35+16.45 = 101.45 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 101.45 }{ 2 } = 50.72 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.72 * (50.72-50)(50.72-35)(50.72-16.45) } ; ; T = sqrt{ 19776.49 } = 140.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 140.63 }{ 50 } = 5.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 140.63 }{ 35 } = 8.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 140.63 }{ 16.45 } = 17.1 ; ;

6. 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{ 50**2-35**2-16.45**2 }{ 2 * 35 * 16.45 } ) = 150° 45'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 35**2-50**2-16.45**2 }{ 2 * 50 * 16.45 } ) = 20° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16.45**2-50**2-35**2 }{ 2 * 35 * 50 } ) = 9° 14'55" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 140.63 }{ 50.72 } = 2.77 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 150° 45'5" } = 51.17 ; ;




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