Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=507.5087925929 and with side c=62.49223370368

#1 Obtuse scalene triangle.

Sides: a = 336.066   b = 285   c = 507.5087925929

Area: T = 45190.49770472
Perimeter: p = 1128.574392593
Semiperimeter: s = 564.2876962965

Angle ∠ A = α = 38.67326200297° = 38°40'21″ = 0.67549645499 rad
Angle ∠ B = β = 32° = 0.55985053606 rad
Angle ∠ C = γ = 109.327737997° = 109°19'39″ = 1.90881227431 rad

Height: ha = 268.9388226701
Height: hb = 317.1266295068
Height: hc = 178.0887847454

Median: ma = 375.7122068413
Median: mb = 406.1365538482
Median: mc = 180.8088197983

Inradius: r = 80.08442479327
Circumradius: R = 268.9098887859

Vertex coordinates: A[507.5087925929; 0] B[0; 0] C[2855.000131483; 178.0887847454]
Centroid: CG[264.1699352471; 59.36326158179]
Coordinates of the circumscribed circle: U[253.7543962965; -898.9995294895]
Coordinates of the inscribed circle: I[279.2876962964; 80.08442479327]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.327737997° = 141°19'39″ = 0.67549645499 rad
∠ B' = β' = 148° = 0.55985053606 rad
∠ C' = γ' = 70.67326200297° = 70°40'21″ = 1.90881227431 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 = 336.07 ; ; b = 285 ; ; c = 507.51 ; ;

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

p = a+b+c = 336.07+285+507.51 = 1128.57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1128.57 }{ 2 } = 564.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 564.29 * (564.29-336.07)(564.29-285)(564.29-507.51) } ; ; T = sqrt{ 2042181023.37 } = 45190.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45190.5 }{ 336.07 } = 268.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45190.5 }{ 285 } = 317.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45190.5 }{ 507.51 } = 178.09 ; ;

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{ 336.07**2-285**2-507.51**2 }{ 2 * 285 * 507.51 } ) = 38° 40'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 285**2-336.07**2-507.51**2 }{ 2 * 336.07 * 507.51 } ) = 32° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 507.51**2-336.07**2-285**2 }{ 2 * 285 * 336.07 } ) = 109° 19'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45190.5 }{ 564.29 } = 80.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 336.07 }{ 2 * sin 38° 40'21" } = 268.91 ; ;





#2 Obtuse scalene triangle.

Sides: a = 336.066   b = 285   c = 62.49223370368

Area: T = 5564.563289262
Perimeter: p = 683.5588337037
Semiperimeter: s = 341.7799168518

Angle ∠ A = α = 141.327737997° = 141°19'39″ = 2.46766281037 rad
Angle ∠ B = β = 32° = 0.55985053606 rad
Angle ∠ C = γ = 6.67326200297° = 6°40'21″ = 0.11664591893 rad

Height: ha = 33.11658932628
Height: hb = 39.05495641587
Height: hc = 178.0887847454

Median: ma = 119.7088216114
Median: mb = 195.2354664627
Median: mc = 310.0110250042

Inradius: r = 16.28111645799
Circumradius: R = 268.9098887859

Vertex coordinates: A[62.49223370368; 0] B[0; 0] C[2855.000131483; 178.0887847454]
Centroid: CG[115.831082284; 59.36326158179]
Coordinates of the circumscribed circle: U[31.24661685184; 267.0877376943]
Coordinates of the inscribed circle: I[56.77991685184; 16.28111645799]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 38.67326200297° = 38°40'21″ = 2.46766281037 rad
∠ B' = β' = 148° = 0.55985053606 rad
∠ C' = γ' = 173.327737997° = 173°19'39″ = 0.11664591893 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 336.07 ; ; b = 285 ; ; beta = 32° ; ; ; ; b**2 = a**2 + c**2 - 2bc cos( beta ) ; ; 285**2 = 336.07**2 + c**2 -2 * 285 * c * cos (32° ) ; ; ; ; c**2 -570c +31715.356 =0 ; ; p=1; q=-570.000262966; r=31715.356356 ; ; D = q**2 - 4pr = 570**2 - 4 * 1 * 31715.356 = 198038.874357 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 570 ± sqrt{ 198038.87 } }{ 2 } ; ; c_{1,2} = 285.000131483 ± 222.507794446 ; ;
c_{1} = 507.507925929 ; ; c_{2} = 62.4923370368 ; ; ; ; (c -507.507925929) (c -62.4923370368) = 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 = 336.07 ; ; b = 285 ; ; c = 62.49 ; ;

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

p = a+b+c = 336.07+285+62.49 = 683.56 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 683.56 }{ 2 } = 341.78 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 341.78 * (341.78-336.07)(341.78-285)(341.78-62.49) } ; ; T = sqrt{ 30964360.19 } = 5564.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5564.56 }{ 336.07 } = 33.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5564.56 }{ 285 } = 39.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5564.56 }{ 62.49 } = 178.09 ; ;

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{ 336.07**2-285**2-62.49**2 }{ 2 * 285 * 62.49 } ) = 141° 19'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 285**2-336.07**2-62.49**2 }{ 2 * 336.07 * 62.49 } ) = 32° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 62.49**2-336.07**2-285**2 }{ 2 * 285 * 336.07 } ) = 6° 40'21" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5564.56 }{ 341.78 } = 16.28 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 336.07 }{ 2 * sin 141° 19'39" } = 268.91 ; ;




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

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