Triangle calculator SSA

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Triangle has two solutions with side c=25.9532940139 and with side c=10.27216531758

#1 Obtuse scalene triangle.

Sides: a = 18.9   b = 9.52   c = 25.9532940139

Area: T = 70.06765817729
Perimeter: p = 54.3732940139
Semiperimeter: s = 27.18664700695

Angle ∠ A = α = 34.55334941996° = 34°33'13″ = 0.60330722419 rad
Angle ∠ B = β = 16.6° = 16°36' = 0.29897246558 rad
Angle ∠ C = γ = 128.84765058° = 128°50'47″ = 2.24987957559 rad

Height: ha = 7.41444530977
Height: hb = 14.72198701204
Height: hc = 5.4399510144

Median: ma = 17.11111148359
Median: mb = 22.19774086535
Median: mc = 7.45219409912

Inradius: r = 2.57772592615
Circumradius: R = 16.66215114337

Vertex coordinates: A[25.9532940139; 0] B[0; 0] C[18.11222966574; 5.4399510144]
Centroid: CG[14.68884122655; 1.87998367147]
Coordinates of the circumscribed circle: U[12.97664700695; -10.45107027415]
Coordinates of the inscribed circle: I[17.66664700695; 2.57772592615]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.44765058° = 145°26'47″ = 0.60330722419 rad
∠ B' = β' = 163.4° = 163°24' = 0.29897246558 rad
∠ C' = γ' = 51.15334941996° = 51°9'13″ = 2.24987957559 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 = 18.9 ; ; b = 9.52 ; ; c = 25.95 ; ;

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

p = a+b+c = 18.9+9.52+25.95 = 54.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54.37 }{ 2 } = 27.19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.19 * (27.19-18.9)(27.19-9.52)(27.19-25.95) } ; ; T = sqrt{ 4909.33 } = 70.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 70.07 }{ 18.9 } = 7.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 70.07 }{ 9.52 } = 14.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 70.07 }{ 25.95 } = 5.4 ; ;

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{ 18.9**2-9.52**2-25.95**2 }{ 2 * 9.52 * 25.95 } ) = 34° 33'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.52**2-18.9**2-25.95**2 }{ 2 * 18.9 * 25.95 } ) = 16° 36' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25.95**2-18.9**2-9.52**2 }{ 2 * 9.52 * 18.9 } ) = 128° 50'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 70.07 }{ 27.19 } = 2.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.9 }{ 2 * sin 34° 33'13" } = 16.66 ; ;





#2 Obtuse scalene triangle.

Sides: a = 18.9   b = 9.52   c = 10.27216531758

Area: T = 27.7310947759
Perimeter: p = 38.69216531758
Semiperimeter: s = 19.34658265879

Angle ∠ A = α = 145.44765058° = 145°26'47″ = 2.53985204117 rad
Angle ∠ B = β = 16.6° = 16°36' = 0.29897246558 rad
Angle ∠ C = γ = 17.95334941996° = 17°57'13″ = 0.3133347586 rad

Height: ha = 2.93444918263
Height: hb = 5.82658293611
Height: hc = 5.4399510144

Median: ma = 2.96107650163
Median: mb = 14.44664815606
Median: mc = 14.05550163735

Inradius: r = 1.43334330783
Circumradius: R = 16.66215114337

Vertex coordinates: A[10.27216531758; 0] B[0; 0] C[18.11222966574; 5.4399510144]
Centroid: CG[9.46113166111; 1.87998367147]
Coordinates of the circumscribed circle: U[5.13658265879; 15.85502128855]
Coordinates of the inscribed circle: I[9.82658265879; 1.43334330783]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 34.55334941996° = 34°33'13″ = 2.53985204117 rad
∠ B' = β' = 163.4° = 163°24' = 0.29897246558 rad
∠ C' = γ' = 162.04765058° = 162°2'47″ = 0.3133347586 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 18.9 ; ; b = 9.52 ; ; beta = 16° 36' ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 9.52**2 = 18.9**2 + c**2 -2 * 9.52 * c * cos (16° 36') ; ; ; ; c**2 -36.225c +266.58 =0 ; ; p=1; q=-36.2245933148; r=266.5796 ; ; D = q**2 - 4pr = 36.225**2 - 4 * 1 * 266.58 = 245.902760821 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 36.22 ± sqrt{ 245.9 } }{ 2 } ; ; c_{1,2} = 18.1122966574 ± 7.84064348159 ; ;
c_{1} = 25.952940139 ; ; c_{2} = 10.2716531758 ; ; ; ; (c -25.952940139) (c -10.2716531758) = 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 = 18.9 ; ; b = 9.52 ; ; c = 10.27 ; ;

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

p = a+b+c = 18.9+9.52+10.27 = 38.69 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38.69 }{ 2 } = 19.35 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.35 * (19.35-18.9)(19.35-9.52)(19.35-10.27) } ; ; T = sqrt{ 769.01 } = 27.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.73 }{ 18.9 } = 2.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.73 }{ 9.52 } = 5.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.73 }{ 10.27 } = 5.4 ; ;

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{ 18.9**2-9.52**2-10.27**2 }{ 2 * 9.52 * 10.27 } ) = 145° 26'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.52**2-18.9**2-10.27**2 }{ 2 * 18.9 * 10.27 } ) = 16° 36' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 10.27**2-18.9**2-9.52**2 }{ 2 * 9.52 * 18.9 } ) = 17° 57'13" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.73 }{ 19.35 } = 1.43 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.9 }{ 2 * sin 145° 26'47" } = 16.66 ; ;




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