Triangle calculator SSA

Please enter two sides and a non-included angle
°


Triangle has two solutions with side c=79.27883767368 and with side c=11.35224019669

#1 Obtuse scalene triangle.

Sides: a = 50   b = 40   c = 79.27883767368

Area: T = 837.6122244253
Perimeter: p = 169.2788376737
Semiperimeter: s = 84.63991883684

Angle ∠ A = α = 31.88988308305° = 31°53'20″ = 0.55765650926 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 123.1111169169° = 123°6'40″ = 2.1498695248 rad

Height: ha = 33.50444897701
Height: hb = 41.88106122126
Height: hc = 21.1310913087

Median: ma = 57.59880078562
Median: mb = 63.18664740986
Median: mc = 21.88800078953

Inradius: r = 9.8966269806
Circumradius: R = 47.32440316631

Vertex coordinates: A[79.27883767368; 0] B[0; 0] C[45.31553893518; 21.1310913087]
Centroid: CG[41.53112553629; 7.04436376957]
Coordinates of the circumscribed circle: U[39.63991883684; -25.85114742006]
Coordinates of the inscribed circle: I[44.63991883684; 9.8966269806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.1111169169° = 148°6'40″ = 0.55765650926 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 56.88988308305° = 56°53'20″ = 2.1498695248 rad




How did we calculate this triangle?

1. Use Law of Cosines

a = 50 ; ; b = 40 ; ; beta = 25° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 40**2 = 50**2 + c**2 -2 * 50 * c * cos (25° ) ; ; ; ; c**2 -90.631c +900 =0 ; ; p=1; q=-90.631; r=900 ; ; D = q**2 - 4pr = 90.631**2 - 4 * 1 * 900 = 4613.93804843 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 90.63 ± sqrt{ 4613.94 } }{ 2 } ; ; c_{1,2} = 45.31538935 ± 33.9629873849 ; ; c_{1} = 79.2783767349 ; ; c_{2} = 11.3524019651 ; ; ; ; text{ Factored form: } ; ; (c -79.2783767349) (c -11.3524019651) = 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 = 40 ; ; c = 79.28 ; ;

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

p = a+b+c = 50+40+79.28 = 169.28 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 169.28 }{ 2 } = 84.64 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 84.64 * (84.64-50)(84.64-40)(84.64-79.28) } ; ; T = sqrt{ 701594.27 } = 837.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 837.61 }{ 50 } = 33.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 837.61 }{ 40 } = 41.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 837.61 }{ 79.28 } = 21.13 ; ;

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{ 40**2+79.28**2-50**2 }{ 2 * 40 * 79.28 } ) = 31° 53'20" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+79.28**2-40**2 }{ 2 * 50 * 79.28 } ) = 25° ; ; gamma = 180° - alpha - beta = 180° - 31° 53'20" - 25° = 123° 6'40" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 837.61 }{ 84.64 } = 9.9 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 50 }{ 2 * sin 31° 53'20" } = 47.32 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 79.28**2 - 50**2 } }{ 2 } = 57.598 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 79.28**2+2 * 50**2 - 40**2 } }{ 2 } = 63.186 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 50**2 - 79.28**2 } }{ 2 } = 21.88 ; ;







#2 Obtuse scalene triangle.

Sides: a = 50   b = 40   c = 11.35224019669

Area: T = 119.9433309646
Perimeter: p = 101.3522401967
Semiperimeter: s = 50.67662009835

Angle ∠ A = α = 148.1111169169° = 148°6'40″ = 2.5855027561 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 6.88988308305° = 6°53'20″ = 0.12202327796 rad

Height: ha = 4.79877323858
Height: hb = 5.99771654823
Height: hc = 21.1310913087

Median: ma = 15.47438009296
Median: mb = 30.2439684443
Median: mc = 44.92197144069

Inradius: r = 2.36768567753
Circumradius: R = 47.32440316631

Vertex coordinates: A[11.35224019669; 0] B[0; 0] C[45.31553893518; 21.1310913087]
Centroid: CG[18.88992637729; 7.04436376957]
Coordinates of the circumscribed circle: U[5.67662009835; 46.98223872876]
Coordinates of the inscribed circle: I[10.67662009835; 2.36768567753]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 31.88988308305° = 31°53'20″ = 2.5855027561 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 173.1111169169° = 173°6'40″ = 0.12202327796 rad

Calculate another triangle

How did we calculate this triangle?

1. Use Law of Cosines

a = 50 ; ; b = 40 ; ; beta = 25° ; ; ; ; b**2 = a**2 + c**2 - 2ac cos beta ; ; 40**2 = 50**2 + c**2 -2 * 50 * c * cos (25° ) ; ; ; ; c**2 -90.631c +900 =0 ; ; p=1; q=-90.631; r=900 ; ; D = q**2 - 4pr = 90.631**2 - 4 * 1 * 900 = 4613.93804843 ; ; D>0 ; ; ; ; c_{1,2} = fraction{ -q ± sqrt{ D } }{ 2p } = fraction{ 90.63 ± sqrt{ 4613.94 } }{ 2 } ; ; c_{1,2} = 45.31538935 ± 33.9629873849 ; ; c_{1} = 79.2783767349 ; ; c_{2} = 11.3524019651 ; ; ; ; text{ Factored form: } ; ; (c -79.2783767349) (c -11.3524019651) = 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 = 40 ; ; c = 11.35 ; ;

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

p = a+b+c = 50+40+11.35 = 101.35 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 101.35 }{ 2 } = 50.68 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 50.68 * (50.68-50)(50.68-40)(50.68-11.35) } ; ; T = sqrt{ 14386.4 } = 119.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.94 }{ 50 } = 4.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.94 }{ 40 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.94 }{ 11.35 } = 21.13 ; ;

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{ 40**2+11.35**2-50**2 }{ 2 * 40 * 11.35 } ) = 148° 6'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+11.35**2-40**2 }{ 2 * 50 * 11.35 } ) = 25° ; ; gamma = 180° - alpha - beta = 180° - 148° 6'40" - 25° = 6° 53'20" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.94 }{ 50.68 } = 2.37 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 50 }{ 2 * sin 148° 6'40" } = 47.32 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 11.35**2 - 50**2 } }{ 2 } = 15.474 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.35**2+2 * 50**2 - 40**2 } }{ 2 } = 30.24 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 40**2+2 * 50**2 - 11.35**2 } }{ 2 } = 44.92 ; ;
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.