Triangle calculator SSA

Please enter two sides and a non-included angle
°


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?

1. Use Law of Cosines

a = 18.9 ; ; b = 9.52 ; ; beta = 16° 36' ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 9.52**2 = 18.9**2 + c**2 -2 * 18.9 * c * cos (16° 36') ; ; ; ; c**2 -36.225c +266.58 =0 ; ; p=1; q=-36.225; r=266.58 ; ; 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} = 18.11229666 ± 7.84064348159 ; ;
c_{1} = 25.9529401416 ; ; c_{2} = 10.2716531784 ; ; ; ; text{ Factored form: } ; ; (c -25.9529401416) (c -10.2716531784) = 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 = 25.95 ; ;

2. 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 ; ;

3. Semiperimeter of the triangle

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

4. 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 ; ;

5. 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 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 9.52**2+25.95**2-18.9**2 }{ 2 * 9.52 * 25.95 } ) = 34° 33'13" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.9**2+25.95**2-9.52**2 }{ 2 * 18.9 * 25.95 } ) = 16° 36' ; ; gamma = 180° - alpha - beta = 180° - 34° 33'13" - 16° 36' = 128° 50'47" ; ;

7. Inradius

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

8. Circumradius

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

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.52**2+2 * 25.95**2 - 18.9**2 } }{ 2 } = 17.111 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.95**2+2 * 18.9**2 - 9.52**2 } }{ 2 } = 22.197 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.52**2+2 * 18.9**2 - 25.95**2 } }{ 2 } = 7.452 ; ;







#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 - 2ac cos beta ; ; 9.52**2 = 18.9**2 + c**2 -2 * 18.9 * c * cos (16° 36') ; ; ; ; c**2 -36.225c +266.58 =0 ; ; p=1; q=-36.225; r=266.58 ; ; 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} = 18.11229666 ± 7.84064348159 ; ; : Nr. 1
c_{1} = 25.9529401416 ; ; c_{2} = 10.2716531784 ; ; ; ; text{ Factored form: } ; ; (c -25.9529401416) (c -10.2716531784) = 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 = 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 9.52**2+10.27**2-18.9**2 }{ 2 * 9.52 * 10.27 } ) = 145° 26'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 18.9**2+10.27**2-9.52**2 }{ 2 * 18.9 * 10.27 } ) = 16° 36' ; ; gamma = 180° - alpha - beta = 180° - 145° 26'47" - 16° 36' = 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 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.52**2+2 * 10.27**2 - 18.9**2 } }{ 2 } = 2.961 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.27**2+2 * 18.9**2 - 9.52**2 } }{ 2 } = 14.446 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.52**2+2 * 18.9**2 - 10.27**2 } }{ 2 } = 14.055 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.