Triangle calculator SSA

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Triangle has two solutions with side c=161.3632738659 and with side c=38.15500713929

#1 Obtuse scalene triangle.

Sides: a = 100   b = 62   c = 161.3632738659

Area: T = 562.8054782127
Perimeter: p = 323.3632738659
Semiperimeter: s = 161.681136933

Angle ∠ A = α = 6.46600518551° = 6°27'36″ = 0.11327491747 rad
Angle ∠ B = β = 4° = 0.07698131701 rad
Angle ∠ C = γ = 169.5439948145° = 169°32'24″ = 2.95990303088 rad

Height: ha = 11.25660956425
Height: hb = 18.15549929719
Height: hc = 6.97656473744

Median: ma = 111.5399081553
Median: mb = 130.6066151133
Median: mc = 20.31105057326

Inradius: r = 3.4810950121
Circumradius: R = 444.4033197812

Vertex coordinates: A[161.3632738659; 0] B[0; 0] C[99.7566405026; 6.97656473744]
Centroid: CG[87.04397145617; 2.32552157915]
Coordinates of the circumscribed circle: U[80.68113693295; -437.0187984606]
Coordinates of the inscribed circle: I[99.68113693295; 3.4810950121]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.5439948145° = 173°32'24″ = 0.11327491747 rad
∠ B' = β' = 176° = 0.07698131701 rad
∠ C' = γ' = 10.46600518551° = 10°27'36″ = 2.95990303088 rad




How did we calculate this triangle?

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 = 100 ; ; b = 62 ; ; c = 161.36 ; ;

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

p = a+b+c = 100+62+161.36 = 323.36 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 323.36 }{ 2 } = 161.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 161.68 * (161.68-100)(161.68-62)(161.68-161.36) } ; ; T = sqrt{ 316749.22 } = 562.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 562.8 }{ 100 } = 11.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 562.8 }{ 62 } = 18.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 562.8 }{ 161.36 } = 6.98 ; ;

5. 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{ 100**2-62**2-161.36**2 }{ 2 * 62 * 161.36 } ) = 6° 27'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 62**2-100**2-161.36**2 }{ 2 * 100 * 161.36 } ) = 4° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 161.36**2-100**2-62**2 }{ 2 * 62 * 100 } ) = 169° 32'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 562.8 }{ 161.68 } = 3.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 6° 27'36" } = 444.4 ; ;





#2 Obtuse scalene triangle.

Sides: a = 100   b = 62   c = 38.15500713929

Area: T = 133.0610722673
Perimeter: p = 200.1550071393
Semiperimeter: s = 100.0755035696

Angle ∠ A = α = 173.5439948145° = 173°32'24″ = 3.02988434789 rad
Angle ∠ B = β = 4° = 0.07698131701 rad
Angle ∠ C = γ = 2.46600518551° = 2°27'36″ = 0.04329360046 rad

Height: ha = 2.66112144535
Height: hb = 4.29222813765
Height: hc = 6.97656473744

Median: ma = 12.23657661649
Median: mb = 69.04113931902
Median: mc = 80.98223623586

Inradius: r = 1.33296095449
Circumradius: R = 444.4033197812

Vertex coordinates: A[38.15500713929; 0] B[0; 0] C[99.7566405026; 6.97656473744]
Centroid: CG[45.9698825473; 2.32552157915]
Coordinates of the circumscribed circle: U[19.07550356965; 443.994363198]
Coordinates of the inscribed circle: I[38.07550356965; 1.33296095449]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 6.46600518551° = 6°27'36″ = 3.02988434789 rad
∠ B' = β' = 176° = 0.07698131701 rad
∠ C' = γ' = 177.5439948145° = 177°32'24″ = 0.04329360046 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 100 ; ; b = 62 ; ; beta = 4° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 62**2 = 100**2 + c**2 -2 * 62 * c * cos (4° ) ; ; ; ; c**2 -199.513c +6156 =0 ; ; p=1; q=-199.512810052; r=6156 ; ; D = q**2 - 4pr = 199.513**2 - 4 * 1 * 6156 = 15181.3613748 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 199.51 ± sqrt{ 15181.36 } }{ 2 } ; ; c_{1,2} = 99.756405026 ± 61.6063336331 ; ; c_{1} = 161.362738659 ; ;
c_{2} = 38.1500713929 ; ; ; ; (c -161.362738659) (c -38.1500713929) = 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 = 100 ; ; b = 62 ; ; c = 38.15 ; ;

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

p = a+b+c = 100+62+38.15 = 200.15 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 200.15 }{ 2 } = 100.08 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 100.08 * (100.08-100)(100.08-62)(100.08-38.15) } ; ; T = sqrt{ 17705.16 } = 133.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 133.06 }{ 100 } = 2.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 133.06 }{ 62 } = 4.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 133.06 }{ 38.15 } = 6.98 ; ;

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{ 100**2-62**2-38.15**2 }{ 2 * 62 * 38.15 } ) = 173° 32'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 62**2-100**2-38.15**2 }{ 2 * 100 * 38.15 } ) = 4° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 38.15**2-100**2-62**2 }{ 2 * 62 * 100 } ) = 2° 27'36" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 133.06 }{ 100.08 } = 1.33 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100 }{ 2 * sin 173° 32'24" } = 444.4 ; ;




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